Taxonomy for Mathematics Articles-9th Class: Difference between revisions
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!Topic | !Topic | ||
!Chapters | !Chapters | ||
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!'''अध्याय''' | !'''अध्याय''' | ||
!विषय | !विषय | ||
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|Number Systems | |Number Systems | ||
|Number Systems | |Number Systems | ||
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|संख्या पद्धति | |संख्या पद्धति | ||
|[[संख्या पद्धति]] | |[[संख्या पद्धति]] | ||
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|Number Line | |Number Line | ||
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|[[संख्या रेखा]] | |[[संख्या रेखा]] | ||
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|Numbers | |Numbers | ||
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|[[संख्या]] | |[[संख्या]] | ||
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|Whole Numbers | |Whole Numbers | ||
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|[[पूर्ण संख्याएँ]] | |[[पूर्ण संख्याएँ]] | ||
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|Integers | |Integers | ||
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|[[पूर्णांक]] | |[[पूर्णांक]] | ||
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|Rational Numbers | |Rational Numbers | ||
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|[[परिमेय संख्याएँ]] | |[[परिमेय संख्याएँ]] | ||
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|Natural Numbers | |Natural Numbers | ||
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|[[प्राकृतिक संख्याएँ]] | |[[प्राकृतिक संख्याएँ]] | ||
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|Fractions | |Fractions | ||
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|[[भिन्न]] | |[[भिन्न]] | ||
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|Irrational Numbers | |Irrational Numbers | ||
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|[[अपरिमेय संख्याएँ]] | |[[अपरिमेय संख्याएँ]] | ||
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|Pythogoras theorem | |Pythogoras theorem | ||
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|[[पाइथागोरस प्रमेय]] | |[[पाइथागोरस प्रमेय]] | ||
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|Terminating decimal expansions | |Terminating decimal expansions | ||
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|[[दशमलव प्रसार को सांत करना]] | |[[दशमलव प्रसार को सांत करना]] | ||
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|Non-terminating recurring decimal expansions | |Non-terminating recurring decimal expansions | ||
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|[[अनवसानी(असांत) आवर्ती दशमलव प्रसार]] | |[[अनवसानी(असांत) आवर्ती दशमलव प्रसार]] | ||
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|Process of successive magnification | |Process of successive magnification | ||
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|[[उत्तरोत्तर आवर्धन प्रक्रम]] | |[[उत्तरोत्तर आवर्धन प्रक्रम]] | ||
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|Degree of accuracy | |Degree of accuracy | ||
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|[[परिशुद्धता मात्रा]] | |[[परिशुद्धता मात्रा]] | ||
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|Real Numbers | |Real Numbers | ||
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|[[वास्तविक संख्याएँ]] | |[[वास्तविक संख्याएँ]] | ||
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|Rationalising the denominator | |Rationalising the denominator | ||
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|[[हर का परिमेयकरण]] | |[[हर का परिमेयकरण]] | ||
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|base and exponents | |base and exponents | ||
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|[[आधार और घातांक]] | |[[आधार और घातांक]] | ||
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|Real Numbers and their Decimal Expansions | |Real Numbers and their Decimal Expansions | ||
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|[[वास्तविक संख्याएँ और उनके दशमलव प्रसार]] | |[[वास्तविक संख्याएँ और उनके दशमलव प्रसार]] | ||
| Line 117: | Line 136: | ||
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|Real Numbers representation on the Number Line | |Real Numbers representation on the Number Line | ||
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|[[संख्या रेखा पर वास्तविक संख्याओं का निरूपण]] | |[[संख्या रेखा पर वास्तविक संख्याओं का निरूपण]] | ||
| Line 123: | Line 143: | ||
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|Operations on Real Numbers | |Operations on Real Numbers | ||
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|[[वास्तविक संख्याओं पर संक्रियाएँ]] | |[[वास्तविक संख्याओं पर संक्रियाएँ]] | ||
| Line 129: | Line 150: | ||
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|Laws of Exponents for Real Numbers | |Laws of Exponents for Real Numbers | ||
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|[[वास्तविक संख्याओं के लिए घातांक-नियम]] | |[[वास्तविक संख्याओं के लिए घातांक-नियम]] | ||
|- | |- | ||
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| Line 141: | Line 164: | ||
|Poynomials | |Poynomials | ||
|Algebraic Expressions | |Algebraic Expressions | ||
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|बहुपद | |बहुपद | ||
|[[बीजीय व्यंजक]] | |[[बीजीय व्यंजक]] | ||
| Line 147: | Line 171: | ||
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|Factorisation | |Factorisation | ||
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|[[गुणनखंडन]] | |[[गुणनखंडन]] | ||
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|Factor Theorem | |Factor Theorem | ||
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|[[गुणनखंड प्रमेय]] | |[[गुणनखंड प्रमेय]] | ||
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|Variables | |Variables | ||
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|[[चर]] | |[[चर]] | ||
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|Constant | |Constant | ||
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|[[अचर]] | |[[अचर]] | ||
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|Terms of Polynomial | |Terms of Polynomial | ||
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|[[बहुपद के पद]] | |[[बहुपद के पद]] | ||
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|Coefficient of Polynomial | |Coefficient of Polynomial | ||
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|[[बहुपद के गुणांक]] | |[[बहुपद के गुणांक]] | ||
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|Constant Polynomials | |Constant Polynomials | ||
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|[[अचर बहुपद]] | |[[अचर बहुपद]] | ||
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|Zero Polynomial | |Zero Polynomial | ||
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|[[शून्य बहुपद]] | |[[शून्य बहुपद]] | ||
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|Monomial | |Monomial | ||
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|[[एकपद]] | |[[एकपद]] | ||
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|Binomial | |Binomial | ||
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|[[द्विपद]] | |[[द्विपद]] | ||
| Line 207: | Line 241: | ||
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|Trinomial | |Trinomial | ||
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|[[त्रिपद]] | |[[त्रिपद]] | ||
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|Degree of the polynomial | |Degree of the polynomial | ||
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|[[बहुपद की घात]] | |[[बहुपद की घात]] | ||
| Line 219: | Line 255: | ||
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|Linear Polynomial | |Linear Polynomial | ||
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|[[रैखिक बहुपद]] | |[[रैखिक बहुपद]] | ||
| Line 225: | Line 262: | ||
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|Quadratic Polynomial | |Quadratic Polynomial | ||
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|[[द्विघाती बहुपद]] | |[[द्विघाती बहुपद]] | ||
| Line 231: | Line 269: | ||
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|Cubic Polynomial | |Cubic Polynomial | ||
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|[[त्रिघाती बहुपद]] | |[[त्रिघाती बहुपद]] | ||
| Line 237: | Line 276: | ||
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|Dividend | |Dividend | ||
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|[[भाज्य]] | |[[भाज्य]] | ||
| Line 243: | Line 283: | ||
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|Divisor | |Divisor | ||
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|[[भाजक]] | |[[भाजक]] | ||
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|Quotient | |Quotient | ||
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|[[भागफल]] | |[[भागफल]] | ||
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|Remainder | |Remainder | ||
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|[[शेषफल]] | |[[शेषफल]] | ||
| Line 261: | Line 304: | ||
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|Polynomials | |Polynomials | ||
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|[[बहुपद]] | |[[बहुपद]] | ||
| Line 267: | Line 311: | ||
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|Polynomials in one variable | |Polynomials in one variable | ||
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|[[एक चर वाले बहुपद]] | |[[एक चर वाले बहुपद]] | ||
| Line 273: | Line 318: | ||
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|Zeroes of a Polynomial | |Zeroes of a Polynomial | ||
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|[[बहुपद के शून्यक]] | |[[बहुपद के शून्यक]] | ||
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|Remainder Theorem | |Remainder Theorem | ||
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|[[शेषफल प्रमेय]] | |[[शेषफल प्रमेय]] | ||
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|Factorisation Of Polynomials | |Factorisation Of Polynomials | ||
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|[[बहुपदों का गुणनखंडन]] | |[[बहुपदों का गुणनखंडन]] | ||
| Line 291: | Line 339: | ||
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|Algebraic Identities | |Algebraic Identities | ||
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|[[बीजीय सर्वसमिकाएँ]] | |[[बीजीय सर्वसमिकाएँ]] | ||
|- | |- | ||
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| Line 303: | Line 353: | ||
|Coordinate Geometry | |Coordinate Geometry | ||
|Coordiante Plane | |Coordiante Plane | ||
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|निर्देशांक ज्यामिति | |निर्देशांक ज्यामिति | ||
|[[निर्देशांक तल]] | |[[निर्देशांक तल]] | ||
| Line 309: | Line 360: | ||
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|Coordinate Axes | |Coordinate Axes | ||
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|[[निर्देशांक अक्ष]] | |[[निर्देशांक अक्ष]] | ||
| Line 315: | Line 367: | ||
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|Quadrants | |Quadrants | ||
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|[[चतुर्थाँश]] | |[[चतुर्थाँश]] | ||
| Line 321: | Line 374: | ||
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|Abscissa | |Abscissa | ||
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|[[भुज]] | |[[भुज]] | ||
| Line 327: | Line 381: | ||
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|Ordinate | |Ordinate | ||
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|[[कोटि]] | |[[कोटि]] | ||
| Line 333: | Line 388: | ||
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|Origin | |Origin | ||
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|[[मूल-बिन्दु]] | |[[मूल-बिन्दु]] | ||
| Line 339: | Line 395: | ||
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|Coordinate Geometry | |Coordinate Geometry | ||
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|[[निर्देशांक ज्यामिति]] | |[[निर्देशांक ज्यामिति]] | ||
| Line 345: | Line 402: | ||
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|Cartesian System | |Cartesian System | ||
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|[[कार्टेशियन पद्धति]] | |[[कार्टेशियन पद्धति]] | ||
| Line 351: | Line 409: | ||
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|Plotting a point in the plane | |Plotting a point in the plane | ||
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|[[तल में एक बिन्दु आलेखित करना]] | |[[तल में एक बिन्दु आलेखित करना]] | ||
|- | |- | ||
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| Line 363: | Line 423: | ||
|Linear Equations in two variables | |Linear Equations in two variables | ||
|Linear Equations | |Linear Equations | ||
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|रैखिक समीकरण | |रैखिक समीकरण | ||
|[[रैखिक समीकरण]] | |[[रैखिक समीकरण]] | ||
| Line 369: | Line 430: | ||
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|Solution of a Linear Equation | |Solution of a Linear Equation | ||
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|[[रैखिक समीकरण के हल]] | |[[रैखिक समीकरण के हल]] | ||
| Line 375: | Line 437: | ||
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|Grapha of a Linear equation in two variables | |Grapha of a Linear equation in two variables | ||
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|[[दो चरों वाले रैखिक समीकरण का आलेख]] | |[[दो चरों वाले रैखिक समीकरण का आलेख]] | ||
| Line 381: | Line 444: | ||
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|Equation of Lines parallel to x-axis and y-axis | |Equation of Lines parallel to x-axis and y-axis | ||
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|[[x-अक्ष और y-अक्ष के समानांतर रेखाओं का समीकरण]] | |[[x-अक्ष और y-अक्ष के समानांतर रेखाओं का समीकरण]] | ||
|- | |- | ||
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| Line 393: | Line 458: | ||
|Introduction to Euclid's Geometry | |Introduction to Euclid's Geometry | ||
|Point | |Point | ||
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|यूक्लिड की ज्यामिति | |यूक्लिड की ज्यामिति | ||
|[[बिंदु]] | |[[बिंदु]] | ||
| Line 399: | Line 465: | ||
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|Line | |Line | ||
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|[[रेखा]] | |[[रेखा]] | ||
| Line 405: | Line 472: | ||
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|Straight Line | |Straight Line | ||
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|[[सीधी रेखा]] | |[[सीधी रेखा]] | ||
| Line 411: | Line 479: | ||
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|Surface | |Surface | ||
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|[[पृष्ठ]] | |[[पृष्ठ]] | ||
| Line 417: | Line 486: | ||
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|Plane surface | |Plane surface | ||
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|[[समतल पृष्ठ]] | |[[समतल पृष्ठ]] | ||
| Line 423: | Line 493: | ||
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|Postulate | |Postulate | ||
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|[[अभिधारणा]] | |[[अभिधारणा]] | ||
| Line 429: | Line 500: | ||
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|Axioms | |Axioms | ||
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|[[अभिगृहीत]] | |[[अभिगृहीत]] | ||
| Line 435: | Line 507: | ||
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|Propositions | |Propositions | ||
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|[[साध्य]] | |[[साध्य]] | ||
| Line 441: | Line 514: | ||
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|Euclid's Geometry | |Euclid's Geometry | ||
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|[[यूक्लिड की ज्यामिति]] | |[[यूक्लिड की ज्यामिति]] | ||
| Line 447: | Line 521: | ||
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|Euclid's definitions, axioms and postulates | |Euclid's definitions, axioms and postulates | ||
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|[[यूक्लिड की परिभाषाएँ, अभिगृहीत और अभिधारणाएँ]] | |[[यूक्लिड की परिभाषाएँ, अभिगृहीत और अभिधारणाएँ]] | ||
| Line 453: | Line 528: | ||
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|Equivalent versions of Euclid's fifth postulate | |Equivalent versions of Euclid's fifth postulate | ||
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|[[यूक्लिड की पाँचवीं अभिधारणा के समतुल्य रुपान्तरण]] | |[[यूक्लिड की पाँचवीं अभिधारणा के समतुल्य रुपान्तरण]] | ||
|- | |- | ||
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| Line 465: | Line 542: | ||
|Lines and Angles | |Lines and Angles | ||
|Line Segment | |Line Segment | ||
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|रेखाएँ और कोण | |रेखाएँ और कोण | ||
|[[रेखाखंड]] | |[[रेखाखंड]] | ||
| Line 471: | Line 549: | ||
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|Ray | |Ray | ||
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|[[किरण]] | |[[किरण]] | ||
| Line 477: | Line 556: | ||
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|Collinear Points | |Collinear Points | ||
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|[[संरेख बिंदु]] | |[[संरेख बिंदु]] | ||
| Line 483: | Line 563: | ||
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|Non-collinear Points | |Non-collinear Points | ||
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|[[असंरेख बिंदु]] | |[[असंरेख बिंदु]] | ||
| Line 489: | Line 570: | ||
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|Angle | |Angle | ||
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|[[कोण]] | |[[कोण]] | ||
| Line 495: | Line 577: | ||
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|Arms of the angle | |Arms of the angle | ||
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|[[कोण की भुजाएँ]] | |[[कोण की भुजाएँ]] | ||
| Line 501: | Line 584: | ||
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|Vertex of the angle | |Vertex of the angle | ||
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|[[कोण का शीर्ष]] | |[[कोण का शीर्ष]] | ||
| Line 507: | Line 591: | ||
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|Acute angle | |Acute angle | ||
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|[[न्यून कोण]] | |[[न्यून कोण]] | ||
| Line 513: | Line 598: | ||
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|Right angle | |Right angle | ||
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|[[समकोण]] | |[[समकोण]] | ||
| Line 519: | Line 605: | ||
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|Obtuse angle | |Obtuse angle | ||
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|[[अधिक कोण]] | |[[अधिक कोण]] | ||
| Line 525: | Line 612: | ||
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|Straight angle | |Straight angle | ||
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|[[ऋजु कोण]] | |[[ऋजु कोण]] | ||
| Line 531: | Line 619: | ||
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|Reflex angle | |Reflex angle | ||
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|[[प्रतिवर्ती कोण]] | |[[प्रतिवर्ती कोण]] | ||
| Line 537: | Line 626: | ||
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|Complimentary angles | |Complimentary angles | ||
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|[[पूरक कोण]] | |[[पूरक कोण]] | ||
| Line 543: | Line 633: | ||
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|Supplementary angles | |Supplementary angles | ||
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|[[संपूरक कोण]] | |[[संपूरक कोण]] | ||
| Line 549: | Line 640: | ||
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|Adjacent angles | |Adjacent angles | ||
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|[[आसन्न कोण]] | |[[आसन्न कोण]] | ||
| Line 555: | Line 647: | ||
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|Linear pair of angles | |Linear pair of angles | ||
| | |||
| | | | ||
|[[कोणों का रैखिक युग्म]] | |[[कोणों का रैखिक युग्म]] | ||
| Line 561: | Line 654: | ||
| | | | ||
|Vertically Opposite Angles | |Vertically Opposite Angles | ||
| | |||
| | | | ||
|[[शीर्षाभिमुख कोण]] | |[[शीर्षाभिमुख कोण]] | ||
| Line 567: | Line 661: | ||
| | | | ||
|Linear pair axiom | |Linear pair axiom | ||
| | |||
| | | | ||
|[[रैखिक युग्म अभिगृहीत]] | |[[रैखिक युग्म अभिगृहीत]] | ||
| Line 573: | Line 668: | ||
| | | | ||
|Transversal | |Transversal | ||
| | |||
| | | | ||
|[[तिर्यक् रेखा]] | |[[तिर्यक् रेखा]] | ||
| Line 579: | Line 675: | ||
| | | | ||
|Exterior angles | |Exterior angles | ||
| | |||
| | | | ||
|[[बाह्य कोण]] | |[[बाह्य कोण]] | ||
| Line 585: | Line 682: | ||
| | | | ||
|Interior angles | |Interior angles | ||
| | |||
| | | | ||
|[[अंतः कोण]] | |[[अंतः कोण]] | ||
| Line 591: | Line 689: | ||
| | | | ||
|Corresponding angles | |Corresponding angles | ||
| | |||
| | | | ||
|[[संगत कोण]] | |[[संगत कोण]] | ||
| Line 597: | Line 696: | ||
| | | | ||
|Alternate interior angles | |Alternate interior angles | ||
| | |||
| | | | ||
|[[एकांतर अंतः कोण]] | |[[एकांतर अंतः कोण]] | ||
| Line 603: | Line 703: | ||
| | | | ||
|Alternate exterior angles | |Alternate exterior angles | ||
| | |||
| | | | ||
|[[एकांतर बाह्य कोण]] | |[[एकांतर बाह्य कोण]] | ||
| Line 609: | Line 710: | ||
| | | | ||
|Consecutive interior angles | |Consecutive interior angles | ||
| | |||
| | | | ||
|[[क्रमागत अंतः कोण]] | |[[क्रमागत अंतः कोण]] | ||
| Line 615: | Line 717: | ||
| | | | ||
|Allied angles | |Allied angles | ||
| | |||
| | | | ||
|[[संबंधित कोण]] | |[[संबंधित कोण]] | ||
| Line 621: | Line 724: | ||
| | | | ||
|Co-interior angles | |Co-interior angles | ||
| | |||
| | | | ||
|[[सह-अंतः कोण]] | |[[सह-अंतः कोण]] | ||
| Line 627: | Line 731: | ||
| | | | ||
|Corresponding angles axiom | |Corresponding angles axiom | ||
| | |||
| | | | ||
|[[संगत कोण अभिगृहीत]] | |[[संगत कोण अभिगृहीत]] | ||
| Line 633: | Line 738: | ||
| | | | ||
|Lines and Angles - Definitions | |Lines and Angles - Definitions | ||
| | |||
| | | | ||
|[[रेखाएँ और कोण - परिभाषाएँ]] | |[[रेखाएँ और कोण - परिभाषाएँ]] | ||
| Line 639: | Line 745: | ||
| | | | ||
|Intersecting and Non-Intersecting Lines | |Intersecting and Non-Intersecting Lines | ||
| | |||
| | | | ||
|[[प्रतिच्छेदी और अप्रतिच्छेदी रेखाएँ]] | |[[प्रतिच्छेदी और अप्रतिच्छेदी रेखाएँ]] | ||
| Line 645: | Line 752: | ||
| | | | ||
|Pairs of Angles | |Pairs of Angles | ||
| | |||
| | | | ||
|[[कोणों के युग्म]] | |[[कोणों के युग्म]] | ||
| Line 651: | Line 759: | ||
| | | | ||
|Parallel Lines and a Transversal | |Parallel Lines and a Transversal | ||
| | |||
| | | | ||
|[[समानांतर रेखाएँ और तिर्यक रेखा]] | |[[समानांतर रेखाएँ और तिर्यक रेखा]] | ||
| Line 657: | Line 766: | ||
| | | | ||
|Lines parallel to the same line | |Lines parallel to the same line | ||
| | |||
| | | | ||
|[[एक ही रेखा के समानांतर रेखाएँ]] | |[[एक ही रेखा के समानांतर रेखाएँ]] | ||
| Line 663: | Line 773: | ||
| | | | ||
|Angle sum property of a triangle | |Angle sum property of a triangle | ||
| | |||
| | | | ||
|[[त्रिभुज का कोण योग गुण]] | |[[त्रिभुज का कोण योग गुण]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 675: | Line 787: | ||
|Triangles | |Triangles | ||
|Congruent Figures | |Congruent Figures | ||
| | |||
|त्रिभुज | |त्रिभुज | ||
|[[सर्वांगसम आकृतियाँ]] | |[[सर्वांगसम आकृतियाँ]] | ||
| Line 681: | Line 794: | ||
| | | | ||
|Angle-Side-Angle congruence rule | |Angle-Side-Angle congruence rule | ||
| | |||
| | | | ||
|[[कोण-भुजा-कोण सर्वांगसमता नियम]] | |[[कोण-भुजा-कोण सर्वांगसमता नियम]] | ||
| Line 687: | Line 801: | ||
| | | | ||
|Angle-Angle-Side congruence rule | |Angle-Angle-Side congruence rule | ||
| | |||
| | | | ||
|[[कोण-कोण-भुजा सर्वांगसमता नियम]] | |[[कोण-कोण-भुजा सर्वांगसमता नियम]] | ||
| Line 693: | Line 808: | ||
| | | | ||
|Right angle - Hypotenuse - Side congruence rule | |Right angle - Hypotenuse - Side congruence rule | ||
| | |||
| | | | ||
|[[समकोण - कर्ण - भुजा सर्वांगसमता का नियम]] | |[[समकोण - कर्ण - भुजा सर्वांगसमता का नियम]] | ||
| Line 699: | Line 815: | ||
| | | | ||
|Triangles | |Triangles | ||
| | |||
| | | | ||
|[[त्रिभुज]] | |[[त्रिभुज]] | ||
| Line 705: | Line 822: | ||
| | | | ||
|Congruence of Triangles | |Congruence of Triangles | ||
| | |||
| | | | ||
|[[त्रिभुजों की सर्वांगसमता]] | |[[त्रिभुजों की सर्वांगसमता]] | ||
| Line 711: | Line 829: | ||
| | | | ||
|Criteria for congruence of triangles | |Criteria for congruence of triangles | ||
| | |||
| | | | ||
|[[त्रिभुजों की सर्वांगसमता के लिए कसौटीयाँ]] | |[[त्रिभुजों की सर्वांगसमता के लिए कसौटीयाँ]] | ||
| Line 717: | Line 836: | ||
| | | | ||
|Properties of a Triangle | |Properties of a Triangle | ||
| | |||
| | | | ||
|[[त्रिभुज के गुण]] | |[[त्रिभुज के गुण]] | ||
| Line 723: | Line 843: | ||
| | | | ||
|Inequalities in a Triangle | |Inequalities in a Triangle | ||
| | |||
| | | | ||
|[[त्रिभुज में असमिकाएँ]] | |[[त्रिभुज में असमिकाएँ]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 735: | Line 857: | ||
|Quadrilaterals | |Quadrilaterals | ||
|Collinear points | |Collinear points | ||
| | |||
|चतुर्भुज | |चतुर्भुज | ||
|[[संरेख बिंदु]] | |[[संरेख बिंदु]] | ||
| Line 741: | Line 864: | ||
| | | | ||
|Quadrilaterals | |Quadrilaterals | ||
| | |||
| | | | ||
|[[चतुर्भुज]] | |[[चतुर्भुज]] | ||
| Line 747: | Line 871: | ||
| | | | ||
|Vertices | |Vertices | ||
| | |||
| | | | ||
|[[शीर्ष]] | |[[शीर्ष]] | ||
| Line 753: | Line 878: | ||
| | | | ||
|Trapezium | |Trapezium | ||
| | |||
| | | | ||
|[[समलंब]] | |[[समलंब]] | ||
| Line 759: | Line 885: | ||
| | | | ||
|Parallelogram | |Parallelogram | ||
| | |||
| | | | ||
|[[समानांतर चतुर्भुज]] | |[[समानांतर चतुर्भुज]] | ||
| Line 765: | Line 892: | ||
| | | | ||
|Rectangle | |Rectangle | ||
| | |||
| | | | ||
|[[आयत]] | |[[आयत]] | ||
| Line 771: | Line 899: | ||
| | | | ||
|Rhombus | |Rhombus | ||
| | |||
| | | | ||
|[[समचतुर्भुज]] | |[[समचतुर्भुज]] | ||
| Line 777: | Line 906: | ||
| | | | ||
|Square | |Square | ||
| | |||
| | | | ||
|[[वर्ग]] | |[[वर्ग]] | ||
| Line 783: | Line 913: | ||
| | | | ||
|Kite | |Kite | ||
| | |||
| | | | ||
|[[पतंग]] | |[[पतंग]] | ||
| Line 789: | Line 920: | ||
| | | | ||
|Angle Sum Property of a Quadrilateral | |Angle Sum Property of a Quadrilateral | ||
| | |||
| | | | ||
|[[चतुर्भुज का कोण योग गुण]] | |[[चतुर्भुज का कोण योग गुण]] | ||
| Line 795: | Line 927: | ||
| | | | ||
|Types of Quadrilaterals | |Types of Quadrilaterals | ||
| | |||
| | | | ||
|[[चतुर्भुज के प्रकार]] | |[[चतुर्भुज के प्रकार]] | ||
| Line 801: | Line 934: | ||
| | | | ||
|Properties of a Parallelogram | |Properties of a Parallelogram | ||
| | |||
| | | | ||
|[[समांतर चतुर्भुज के गुण]] | |[[समांतर चतुर्भुज के गुण]] | ||
| Line 807: | Line 941: | ||
| | | | ||
|Condition for a Quadrilateral to be a Parallelogram | |Condition for a Quadrilateral to be a Parallelogram | ||
| | |||
| | | | ||
|[[चतुर्भुज के समांतर चतुर्भुज होने के लिए प्रतिबन्ध]] | |[[चतुर्भुज के समांतर चतुर्भुज होने के लिए प्रतिबन्ध]] | ||
| Line 813: | Line 948: | ||
| | | | ||
|The Mid-point theorem | |The Mid-point theorem | ||
| | |||
| | | | ||
|[[मध्य-बिंदु प्रमेय]] | |[[मध्य-बिंदु प्रमेय]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 825: | Line 962: | ||
|Areas of Parallelograms and Triangles | |Areas of Parallelograms and Triangles | ||
|Planar region | |Planar region | ||
| | |||
|समांतर चतुर्भुजों और त्रिभुजों का क्षेत्रफल | |समांतर चतुर्भुजों और त्रिभुजों का क्षेत्रफल | ||
|[[तलीय क्षेत्र]] | |[[तलीय क्षेत्र]] | ||
| Line 831: | Line 969: | ||
| | | | ||
|Area | |Area | ||
| | |||
| | | | ||
|[[क्षेत्रफल]] | |[[क्षेत्रफल]] | ||
| Line 837: | Line 976: | ||
| | | | ||
|Median of a triangle | |Median of a triangle | ||
| | |||
| | | | ||
|[[त्रिभुज की माध्यिका]] | |[[त्रिभुज की माध्यिका]] | ||
| Line 843: | Line 983: | ||
| | | | ||
|Figures on the same base and between the same parallels | |Figures on the same base and between the same parallels | ||
| | |||
| | | | ||
|[[एक ही आधार पर और एक ही समांतर रेखाओं के बीच आकृतियाँ]] | |[[एक ही आधार पर और एक ही समांतर रेखाओं के बीच आकृतियाँ]] | ||
| Line 849: | Line 990: | ||
| | | | ||
|Parallelograms on the same base and between the same parallels | |Parallelograms on the same base and between the same parallels | ||
| | |||
| | | | ||
|[[एक ही आधार और एक ही समांतर रेखाओं के बीच समांतर चतुर्भुज]] | |[[एक ही आधार और एक ही समांतर रेखाओं के बीच समांतर चतुर्भुज]] | ||
| Line 855: | Line 997: | ||
| | | | ||
|Triangles on the same base and between the same parallels | |Triangles on the same base and between the same parallels | ||
| | |||
| | | | ||
|[[एक ही आधार और एक ही समांतर रेखाओं के बीच स्थित त्रिभुज]] | |[[एक ही आधार और एक ही समांतर रेखाओं के बीच स्थित त्रिभुज]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 867: | Line 1,011: | ||
|Circles | |Circles | ||
|Radius | |Radius | ||
| | |||
|वृत्त | |वृत्त | ||
|[[त्रिज्या]] | |[[त्रिज्या]] | ||
| Line 873: | Line 1,018: | ||
| | | | ||
|Centre of a circle | |Centre of a circle | ||
| | |||
| | | | ||
|[[वृत्त का केंद्र]] | |[[वृत्त का केंद्र]] | ||
| Line 879: | Line 1,025: | ||
| | | | ||
|Diameter | |Diameter | ||
| | |||
| | | | ||
|[[वृत्त का व्यास]] | |[[वृत्त का व्यास]] | ||
| Line 885: | Line 1,032: | ||
| | | | ||
|Interior of the circle | |Interior of the circle | ||
| | |||
| | | | ||
|[[वृत्त का अभ्यंतर]] | |[[वृत्त का अभ्यंतर]] | ||
| Line 891: | Line 1,039: | ||
| | | | ||
|Exterior of the circle | |Exterior of the circle | ||
| | |||
| | | | ||
|[[वृत्त का बहिर्भाग]] | |[[वृत्त का बहिर्भाग]] | ||
| Line 897: | Line 1,046: | ||
| | | | ||
|Arc | |Arc | ||
| | |||
| | | | ||
|[[चाप]] | |[[चाप]] | ||
| Line 903: | Line 1,053: | ||
| | | | ||
|Major arc | |Major arc | ||
| | |||
| | | | ||
|[[दीर्घ चाप]] | |[[दीर्घ चाप]] | ||
| Line 909: | Line 1,060: | ||
| | | | ||
|Minor arc | |Minor arc | ||
| | |||
| | | | ||
|[[लघु चाप]] | |[[लघु चाप]] | ||
| Line 915: | Line 1,067: | ||
| | | | ||
|Semicircle | |Semicircle | ||
| | |||
| | | | ||
|[[अर्धवृत्त]] | |[[अर्धवृत्त]] | ||
| Line 921: | Line 1,074: | ||
| | | | ||
|Circumference | |Circumference | ||
| | |||
| | | | ||
|[[परिकेन्द्र]] | |[[परिकेन्द्र]] | ||
| Line 927: | Line 1,081: | ||
| | | | ||
|Segment | |Segment | ||
| | |||
| | | | ||
|[[वृत्तखंड]] | |[[वृत्तखंड]] | ||
| Line 933: | Line 1,088: | ||
| | | | ||
|Major segment | |Major segment | ||
| | |||
| | | | ||
|[[दीर्घ वृत्तखंड]] | |[[दीर्घ वृत्तखंड]] | ||
| Line 939: | Line 1,095: | ||
| | | | ||
|Minor segment | |Minor segment | ||
| | |||
| | | | ||
|[[लघु वृत्तखंड]] | |[[लघु वृत्तखंड]] | ||
| Line 945: | Line 1,102: | ||
| | | | ||
|Sector | |Sector | ||
| | |||
| | | | ||
|[[त्रिज्यखंड]] | |[[त्रिज्यखंड]] | ||
| Line 951: | Line 1,109: | ||
| | | | ||
|Major sector | |Major sector | ||
| | |||
| | | | ||
|[[दीर्घ त्रिज्यखंड]] | |[[दीर्घ त्रिज्यखंड]] | ||
| Line 957: | Line 1,116: | ||
| | | | ||
|Minor sector | |Minor sector | ||
| | |||
| | | | ||
|[[लघु त्रिज्यखंड]] | |[[लघु त्रिज्यखंड]] | ||
| Line 963: | Line 1,123: | ||
| | | | ||
|Chord | |Chord | ||
| | |||
| | | | ||
|[[जीवा]] | |[[जीवा]] | ||
| Line 969: | Line 1,130: | ||
| | | | ||
|Circumcircle | |Circumcircle | ||
| | |||
| | | | ||
|[[परिवृत्त]] | |[[परिवृत्त]] | ||
| Line 975: | Line 1,137: | ||
| | | | ||
|Circumcentre | |Circumcentre | ||
| | |||
| | | | ||
|[[परिकेन्द्र]] | |[[परिकेन्द्र]] | ||
| Line 981: | Line 1,144: | ||
| | | | ||
|Circumradius | |Circumradius | ||
| | |||
| | | | ||
|[[परित्रिज्या]] | |[[परित्रिज्या]] | ||
| Line 987: | Line 1,151: | ||
| | | | ||
|Circles | |Circles | ||
| | |||
| | | | ||
|[[वृत्त]] | |[[वृत्त]] | ||
| Line 993: | Line 1,158: | ||
| | | | ||
|Circle - related terms | |Circle - related terms | ||
| | |||
| | | | ||
|[[वृत्त - संबंधित पद]] | |[[वृत्त - संबंधित पद]] | ||
| Line 999: | Line 1,165: | ||
| | | | ||
|Angle subtended by a chord at a point | |Angle subtended by a chord at a point | ||
| | |||
| | | | ||
|[[जीवा द्वारा एक बिंदु पर अंतरित कोण]] | |[[जीवा द्वारा एक बिंदु पर अंतरित कोण]] | ||
| Line 1,005: | Line 1,172: | ||
| | | | ||
|Perpendicular from the centre to a chord | |Perpendicular from the centre to a chord | ||
| | |||
| | | | ||
|[[केंद्र से जीवा पर लंब]] | |[[केंद्र से जीवा पर लंब]] | ||
| Line 1,011: | Line 1,179: | ||
| | | | ||
|Circle through three points | |Circle through three points | ||
| | |||
| | | | ||
|[[तीन बिंदुओं से जाने वाला वृत्त]] | |[[तीन बिंदुओं से जाने वाला वृत्त]] | ||
| Line 1,017: | Line 1,186: | ||
| | | | ||
|Equal chords and their distances from the centre | |Equal chords and their distances from the centre | ||
| | |||
| | | | ||
|[[समान जीवाएं और उनकी केंद्र से दूरीयाँ]] | |[[समान जीवाएं और उनकी केंद्र से दूरीयाँ]] | ||
| Line 1,023: | Line 1,193: | ||
| | | | ||
|Angle subtended by an arc of a circle | |Angle subtended by an arc of a circle | ||
| | |||
| | | | ||
|[[एक वृत्त के चाप द्वारा अंतरित कोण]] | |[[एक वृत्त के चाप द्वारा अंतरित कोण]] | ||
| Line 1,029: | Line 1,200: | ||
| | | | ||
|Cyclic Quadrilaterals | |Cyclic Quadrilaterals | ||
| | |||
| | | | ||
|[[चक्रीय चतुर्भुज]] | |[[चक्रीय चतुर्भुज]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,041: | Line 1,214: | ||
|Constructions | |Constructions | ||
|Basic constructions | |Basic constructions | ||
| | |||
|रचनाएँ | |रचनाएँ | ||
|[[आधारभूत रचनाएँ]] | |[[आधारभूत रचनाएँ]] | ||
| Line 1,047: | Line 1,221: | ||
| | | | ||
|Constructions of triangles | |Constructions of triangles | ||
| | |||
| | | | ||
|[[त्रिभुजों की रचनाएँ]] | |[[त्रिभुजों की रचनाएँ]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,059: | Line 1,235: | ||
|Heron's formula | |Heron's formula | ||
|Equilateral triangle | |Equilateral triangle | ||
| | |||
|हीरोन का सूत्र | |हीरोन का सूत्र | ||
|[[समबाहु त्रिभुज]] | |[[समबाहु त्रिभुज]] | ||
| Line 1,065: | Line 1,242: | ||
| | | | ||
|Heron's formula | |Heron's formula | ||
| | |||
| | | | ||
|[[हीरोन का सूत्र]] | |[[हीरोन का सूत्र]] | ||
| Line 1,071: | Line 1,249: | ||
| | | | ||
|Area of Triangle - by Heron's formula | |Area of Triangle - by Heron's formula | ||
| | |||
| | | | ||
|[[त्रिभुज का क्षेत्रफल - हीरोन के सूत्र द्वारा]] | |[[त्रिभुज का क्षेत्रफल - हीरोन के सूत्र द्वारा]] | ||
| Line 1,077: | Line 1,256: | ||
| | | | ||
|Applications of Heron's formula in finding areas of quadrilaterals | |Applications of Heron's formula in finding areas of quadrilaterals | ||
| | |||
| | | | ||
|[[चतुर्भुजों का क्षेत्रफल ज्ञात करने में हीरोन के सूत्र का अनुप्रयोग]] | |[[चतुर्भुजों का क्षेत्रफल ज्ञात करने में हीरोन के सूत्र का अनुप्रयोग]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,089: | Line 1,270: | ||
|Surface Area and Volumes | |Surface Area and Volumes | ||
|Plane figures | |Plane figures | ||
| | |||
|पृष्ठीय क्षेत्रफल और आयतन | |पृष्ठीय क्षेत्रफल और आयतन | ||
|[[समतल आकृतियाँ]] | |[[समतल आकृतियाँ]] | ||
| Line 1,095: | Line 1,277: | ||
| | | | ||
|Solid figures | |Solid figures | ||
| | |||
| | | | ||
|[[ठोस आकृतियाँ]] | |[[ठोस आकृतियाँ]] | ||
| Line 1,101: | Line 1,284: | ||
| | | | ||
|Cuboid | |Cuboid | ||
| | |||
| | | | ||
|[[घनाभ]] | |[[घनाभ]] | ||
| Line 1,107: | Line 1,291: | ||
| | | | ||
|Cube | |Cube | ||
| | |||
| | | | ||
|[[घन]] | |[[घन]] | ||
| Line 1,113: | Line 1,298: | ||
| | | | ||
|Surface area | |Surface area | ||
| | |||
| | | | ||
|[[पृष्ठीय क्षेत्रफल]] | |[[पृष्ठीय क्षेत्रफल]] | ||
| Line 1,119: | Line 1,305: | ||
| | | | ||
|Volume | |Volume | ||
| | |||
| | | | ||
|[[आयतन]] | |[[आयतन]] | ||
| Line 1,125: | Line 1,312: | ||
| | | | ||
|Cylinder | |Cylinder | ||
| | |||
| | | | ||
|[[बेलन]] | |[[बेलन]] | ||
| Line 1,131: | Line 1,319: | ||
| | | | ||
|Prisms | |Prisms | ||
| | |||
| | | | ||
|[[प्रिज्म]] | |[[प्रिज्म]] | ||
| Line 1,137: | Line 1,326: | ||
| | | | ||
|Pyramids | |Pyramids | ||
| | |||
| | | | ||
|[[पिरामिड]] | |[[पिरामिड]] | ||
| Line 1,143: | Line 1,333: | ||
| | | | ||
|Cone | |Cone | ||
| | |||
| | | | ||
|[[शंकु]] | |[[शंकु]] | ||
| Line 1,149: | Line 1,340: | ||
| | | | ||
|Sphere | |Sphere | ||
| | |||
| | | | ||
|[[गोला]] | |[[गोला]] | ||
| Line 1,155: | Line 1,347: | ||
| | | | ||
|Hemisphere | |Hemisphere | ||
| | |||
| | | | ||
|[[अर्धगोला]] | |[[अर्धगोला]] | ||
| Line 1,161: | Line 1,354: | ||
| | | | ||
|Curved surface area | |Curved surface area | ||
| | |||
| | | | ||
|[[वक्र पृष्ठ का क्षेत्रफल]] | |[[वक्र पृष्ठ का क्षेत्रफल]] | ||
| Line 1,167: | Line 1,361: | ||
| | | | ||
|Total surface area | |Total surface area | ||
| | |||
| | | | ||
|[[कुल पृष्ठीय क्षेत्रफल]] | |[[कुल पृष्ठीय क्षेत्रफल]] | ||
| Line 1,173: | Line 1,368: | ||
| | | | ||
|Surface Area and Volumes | |Surface Area and Volumes | ||
| | |||
| | | | ||
|[[पृष्ठीय क्षेत्रफल और आयतन]] | |[[पृष्ठीय क्षेत्रफल और आयतन]] | ||
| Line 1,179: | Line 1,375: | ||
| | | | ||
|Surface Area of a Cuboid and a Cube | |Surface Area of a Cuboid and a Cube | ||
| | |||
| | | | ||
|[[घनाभ और घन के पृष्ठीय क्षेत्रफल]] | |[[घनाभ और घन के पृष्ठीय क्षेत्रफल]] | ||
| Line 1,185: | Line 1,382: | ||
| | | | ||
|Surface Area of a right circular cylinder | |Surface Area of a right circular cylinder | ||
| | |||
| | | | ||
|[[एक लम्ब वृत्तीय बेलन का पृष्ठीय क्षेत्रफल]] | |[[एक लम्ब वृत्तीय बेलन का पृष्ठीय क्षेत्रफल]] | ||
| Line 1,191: | Line 1,389: | ||
| | | | ||
|Surface Area of a right circular cone | |Surface Area of a right circular cone | ||
| | |||
| | | | ||
|[[एक लम्ब वृत्तीय शंकु का पृष्ठीय क्षेत्रफल]] | |[[एक लम्ब वृत्तीय शंकु का पृष्ठीय क्षेत्रफल]] | ||
| Line 1,197: | Line 1,396: | ||
| | | | ||
|Surface area of a sphere | |Surface area of a sphere | ||
| | |||
| | | | ||
|[[गोले का पृष्ठीय क्षेत्रफल]] | |[[गोले का पृष्ठीय क्षेत्रफल]] | ||
| Line 1,203: | Line 1,403: | ||
| | | | ||
|Volume of a cuboid | |Volume of a cuboid | ||
| | |||
| | | | ||
|[[घनाभ का आयतन]] | |[[घनाभ का आयतन]] | ||
| Line 1,209: | Line 1,410: | ||
| | | | ||
|Volume of a cylinder | |Volume of a cylinder | ||
| | |||
| | | | ||
|[[बेलन का आयतन]] | |[[बेलन का आयतन]] | ||
| Line 1,215: | Line 1,417: | ||
| | | | ||
|Volume of a right circular cone | |Volume of a right circular cone | ||
| | |||
| | | | ||
|[[लम्ब वृत्तीय शंकु का आयतन]] | |[[लम्ब वृत्तीय शंकु का आयतन]] | ||
| Line 1,221: | Line 1,424: | ||
| | | | ||
|Volume of a sphere | |Volume of a sphere | ||
| | |||
| | | | ||
|[[गोले का आयतन]] | |[[गोले का आयतन]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,233: | Line 1,438: | ||
|Statistics | |Statistics | ||
|Data | |Data | ||
| | |||
|सांख्यिकी | |सांख्यिकी | ||
|[[आंकड़े]] | |[[आंकड़े]] | ||
| Line 1,239: | Line 1,445: | ||
| | | | ||
|Statistics | |Statistics | ||
| | |||
| | | | ||
|[[सांख्यिकी]] | |[[सांख्यिकी]] | ||
| Line 1,245: | Line 1,452: | ||
| | | | ||
|Primary data | |Primary data | ||
| | |||
| | | | ||
|[[प्राथमिक आंकड़े]] | |[[प्राथमिक आंकड़े]] | ||
| Line 1,251: | Line 1,459: | ||
| | | | ||
|Secondary data | |Secondary data | ||
| | |||
| | | | ||
|[[गौण आंकड़े]] | |[[गौण आंकड़े]] | ||
| Line 1,257: | Line 1,466: | ||
| | | | ||
|Raw data | |Raw data | ||
| | |||
| | | | ||
|[[यथाप्राप्त आंकड़े]] | |[[यथाप्राप्त आंकड़े]] | ||
| Line 1,263: | Line 1,473: | ||
| | | | ||
|frequency distribution table | |frequency distribution table | ||
| | |||
| | | | ||
|[[बारंबारता बंटन सारणी]] | |[[बारंबारता बंटन सारणी]] | ||
| Line 1,269: | Line 1,480: | ||
| | | | ||
|Tally marks | |Tally marks | ||
| | |||
| | | | ||
|[[मिलान चिन्ह]] | |[[मिलान चिन्ह]] | ||
| Line 1,275: | Line 1,487: | ||
| | | | ||
|Class-interval | |Class-interval | ||
| | |||
| | | | ||
|[[वर्ग-अंतराल]] | |[[वर्ग-अंतराल]] | ||
| Line 1,281: | Line 1,494: | ||
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|Class-size | |Class-size | ||
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| | | | ||
|[[वर्ग-माप]] | |[[वर्ग-माप]] | ||
| Line 1,287: | Line 1,501: | ||
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|Class Limit | |Class Limit | ||
| | |||
| | | | ||
|[[वर्ग-सीमा]] | |[[वर्ग-सीमा]] | ||
| Line 1,293: | Line 1,508: | ||
| | | | ||
|Lower Class Limit | |Lower Class Limit | ||
| | |||
| | | | ||
|[[निम्न वर्ग-सीमा]] | |[[निम्न वर्ग-सीमा]] | ||
| Line 1,299: | Line 1,515: | ||
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|Upper Class Limit | |Upper Class Limit | ||
| | |||
| | | | ||
|[[उपरि वर्ग-सीमा]] | |[[उपरि वर्ग-सीमा]] | ||
| Line 1,305: | Line 1,522: | ||
| | | | ||
|Bar graphs | |Bar graphs | ||
| | |||
| | | | ||
|[[दंड आलेख]] | |[[दंड आलेख]] | ||
| Line 1,311: | Line 1,529: | ||
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|Histogram | |Histogram | ||
| | |||
| | | | ||
|[[आयतचित्र]] | |[[आयतचित्र]] | ||
| Line 1,317: | Line 1,536: | ||
| | | | ||
|Frequency polygon | |Frequency polygon | ||
| | |||
| | | | ||
|[[बारंबारता बहुभुज]] | |[[बारंबारता बहुभुज]] | ||
| Line 1,323: | Line 1,543: | ||
| | | | ||
|Central Tendency | |Central Tendency | ||
| | |||
| | | | ||
|[[केंद्रीय प्रवृत्ति]] | |[[केंद्रीय प्रवृत्ति]] | ||
| Line 1,329: | Line 1,550: | ||
| | | | ||
|Collection of data | |Collection of data | ||
| | |||
| | | | ||
|[[आँकड़ों का संग्रह]] | |[[आँकड़ों का संग्रह]] | ||
| Line 1,335: | Line 1,557: | ||
| | | | ||
|Presentation of data | |Presentation of data | ||
| | |||
| | | | ||
|[[आंकड़ों का प्रस्तुतिकरण]] | |[[आंकड़ों का प्रस्तुतिकरण]] | ||
| Line 1,341: | Line 1,564: | ||
| | | | ||
|Graphical representation of data | |Graphical representation of data | ||
| | |||
| | | | ||
|[[आंकड़ों का आलेखीय निरूपण]] | |[[आंकड़ों का आलेखीय निरूपण]] | ||
| Line 1,347: | Line 1,571: | ||
| | | | ||
|Measures of central tendency | |Measures of central tendency | ||
| | |||
| | | | ||
|[[केंद्रीय प्रवृत्ति के माप]] | |[[केंद्रीय प्रवृत्ति के माप]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,359: | Line 1,585: | ||
|Probability | |Probability | ||
|Probability | |Probability | ||
| | |||
|प्रायिकता | |प्रायिकता | ||
|[[प्रायिकता]] | |[[प्रायिकता]] | ||
| Line 1,365: | Line 1,592: | ||
| | | | ||
|Empirical Probability | |Empirical Probability | ||
| | |||
| | | | ||
|[[आनुभविक प्रायिकता]] | |[[आनुभविक प्रायिकता]] | ||
| Line 1,371: | Line 1,599: | ||
| | | | ||
|Event (Probability) | |Event (Probability) | ||
| | |||
| | | | ||
|[[घटना(प्रायिकता)]] | |[[घटना(प्रायिकता)]] | ||
| Line 1,377: | Line 1,606: | ||
| | | | ||
|Probability - an experimental approach | |Probability - an experimental approach | ||
| | |||
| | | | ||
|[[प्रायिकता-एक प्रायोगिक दृष्टिकोण]] | |[[प्रायिकता-एक प्रायोगिक दृष्टिकोण]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,389: | Line 1,620: | ||
|Proofs in Mathematics | |Proofs in Mathematics | ||
|Deductive Reasoning | |Deductive Reasoning | ||
| | |||
|गणित में उपपत्तियाँ | |गणित में उपपत्तियाँ | ||
|[[निगमनिक तर्कण]] | |[[निगमनिक तर्कण]] | ||
| Line 1,395: | Line 1,627: | ||
| | | | ||
|Axioms | |Axioms | ||
| | |||
| | | | ||
|[[अभिगृहीत]] | |[[अभिगृहीत]] | ||
| Line 1,401: | Line 1,634: | ||
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|Mathematically acceptable statements | |Mathematically acceptable statements | ||
| | |||
| | | | ||
|[[गणितीय रूप से स्वीकार्य कथन]] | |[[गणितीय रूप से स्वीकार्य कथन]] | ||
| Line 1,407: | Line 1,641: | ||
| | | | ||
|Theorems, conjectures and axioms | |Theorems, conjectures and axioms | ||
| | |||
| | | | ||
|[[प्रमेय, कंजेक्चर,और अभिगृहीत]] | |[[प्रमेय, कंजेक्चर,और अभिगृहीत]] | ||
| Line 1,413: | Line 1,648: | ||
| | | | ||
|What is a Mathematical Proof | |What is a Mathematical Proof | ||
| | |||
| | | | ||
|[[गणितीय उपपत्ति क्या है?]] | |[[गणितीय उपपत्ति क्या है?]] | ||
| Line 1,419: | Line 1,655: | ||
| | | | ||
|Conjecture | |Conjecture | ||
| | |||
| | | | ||
|[[अनुमान(कंजेक्चर)]] | |[[अनुमान(कंजेक्चर)]] | ||
| Line 1,425: | Line 1,662: | ||
| | | | ||
|Theorem | |Theorem | ||
| | |||
| | | | ||
|[[प्रमेय]] | |[[प्रमेय]] | ||
| Line 1,431: | Line 1,669: | ||
| | | | ||
|Hypothesis | |Hypothesis | ||
| | |||
| | | | ||
|[[परिकल्पना]] | |[[परिकल्पना]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
| Line 1,443: | Line 1,683: | ||
|Mathematical Modelling | |Mathematical Modelling | ||
|Mathematical Modelling | |Mathematical Modelling | ||
| | |||
|गणितीय निदर्शन | |गणितीय निदर्शन | ||
|[[गणितीय निदर्शन]] | |[[गणितीय निदर्शन]] | ||
| Line 1,449: | Line 1,690: | ||
| | | | ||
|Formualtion | |Formualtion | ||
| | |||
| | | | ||
|[[सूत्रण]] | |[[सूत्रण]] | ||
| Line 1,455: | Line 1,697: | ||
| | | | ||
|Solution | |Solution | ||
| | |||
| | | | ||
|[[हल]] | |[[हल]] | ||
| Line 1,461: | Line 1,704: | ||
| | | | ||
|Interpretation | |Interpretation | ||
| | |||
| | | | ||
|[[निर्वचन]] | |[[निर्वचन]] | ||
| Line 1,467: | Line 1,711: | ||
| | | | ||
|Validation | |Validation | ||
| | |||
| | | | ||
|[[मान्यकरण]] | |[[मान्यकरण]] | ||
| Line 1,473: | Line 1,718: | ||
| | | | ||
|Problem statement | |Problem statement | ||
| | |||
| | | | ||
|[[समस्या कथन]] | |[[समस्या कथन]] | ||
| Line 1,479: | Line 1,725: | ||
| | | | ||
|Mathematical description | |Mathematical description | ||
| | |||
| | | | ||
|[[गणितीय वर्णन]] | |[[गणितीय वर्णन]] | ||
| Line 1,485: | Line 1,732: | ||
| | | | ||
|Mathematical Models | |Mathematical Models | ||
| | |||
| | | | ||
|[[गणितीय निदर्श]] | |[[गणितीय निदर्श]] | ||
| Line 1,491: | Line 1,739: | ||
| | | | ||
|The Process of Modelling, its advantages and limitations | |The Process of Modelling, its advantages and limitations | ||
| | |||
| | | | ||
|[[निदर्शन प्रक्रम, इसके लाभ और सीमाएँ]] | |[[निदर्शन प्रक्रम, इसके लाभ और सीमाएँ]] | ||
|} | |} | ||
Revision as of 16:54, 23 August 2023
| S.No | Topic | Chapters | अध्याय | विषय | |
|---|---|---|---|---|---|
| 1 | Number Systems | Number Systems | संख्या पद्धति | संख्या पद्धति | |
| Number Line | संख्या रेखा | ||||
| Numbers | संख्या | ||||
| Whole Numbers | पूर्ण संख्याएँ | ||||
| Integers | पूर्णांक | ||||
| Rational Numbers | परिमेय संख्याएँ | ||||
| Natural Numbers | प्राकृतिक संख्याएँ | ||||
| Fractions | भिन्न | ||||
| Irrational Numbers | अपरिमेय संख्याएँ | ||||
| Pythogoras theorem | पाइथागोरस प्रमेय | ||||
| Terminating decimal expansions | दशमलव प्रसार को सांत करना | ||||
| Non-terminating recurring decimal expansions | अनवसानी(असांत) आवर्ती दशमलव प्रसार | ||||
| Process of successive magnification | उत्तरोत्तर आवर्धन प्रक्रम | ||||
| Degree of accuracy | परिशुद्धता मात्रा | ||||
| Real Numbers | वास्तविक संख्याएँ | ||||
| Rationalising the denominator | हर का परिमेयकरण | ||||
| base and exponents | आधार और घातांक | ||||
| Real Numbers and their Decimal Expansions | वास्तविक संख्याएँ और उनके दशमलव प्रसार | ||||
| Real Numbers representation on the Number Line | संख्या रेखा पर वास्तविक संख्याओं का निरूपण | ||||
| Operations on Real Numbers | वास्तविक संख्याओं पर संक्रियाएँ | ||||
| Laws of Exponents for Real Numbers | वास्तविक संख्याओं के लिए घातांक-नियम | ||||
| 2 | Poynomials | Algebraic Expressions | बहुपद | बीजीय व्यंजक | |
| Factorisation | गुणनखंडन | ||||
| Factor Theorem | गुणनखंड प्रमेय | ||||
| Variables | चर | ||||
| Constant | अचर | ||||
| Terms of Polynomial | बहुपद के पद | ||||
| Coefficient of Polynomial | बहुपद के गुणांक | ||||
| Constant Polynomials | अचर बहुपद | ||||
| Zero Polynomial | शून्य बहुपद | ||||
| Monomial | एकपद | ||||
| Binomial | द्विपद | ||||
| Trinomial | त्रिपद | ||||
| Degree of the polynomial | बहुपद की घात | ||||
| Linear Polynomial | रैखिक बहुपद | ||||
| Quadratic Polynomial | द्विघाती बहुपद | ||||
| Cubic Polynomial | त्रिघाती बहुपद | ||||
| Dividend | भाज्य | ||||
| Divisor | भाजक | ||||
| Quotient | भागफल | ||||
| Remainder | शेषफल | ||||
| Polynomials | बहुपद | ||||
| Polynomials in one variable | एक चर वाले बहुपद | ||||
| Zeroes of a Polynomial | बहुपद के शून्यक | ||||
| Remainder Theorem | शेषफल प्रमेय | ||||
| Factorisation Of Polynomials | बहुपदों का गुणनखंडन | ||||
| Algebraic Identities | बीजीय सर्वसमिकाएँ | ||||
| 3 | Coordinate Geometry | Coordiante Plane | निर्देशांक ज्यामिति | निर्देशांक तल | |
| Coordinate Axes | निर्देशांक अक्ष | ||||
| Quadrants | चतुर्थाँश | ||||
| Abscissa | भुज | ||||
| Ordinate | कोटि | ||||
| Origin | मूल-बिन्दु | ||||
| Coordinate Geometry | निर्देशांक ज्यामिति | ||||
| Cartesian System | कार्टेशियन पद्धति | ||||
| Plotting a point in the plane | तल में एक बिन्दु आलेखित करना | ||||
| 4 | Linear Equations in two variables | Linear Equations | रैखिक समीकरण | रैखिक समीकरण | |
| Solution of a Linear Equation | रैखिक समीकरण के हल | ||||
| Grapha of a Linear equation in two variables | दो चरों वाले रैखिक समीकरण का आलेख | ||||
| Equation of Lines parallel to x-axis and y-axis | x-अक्ष और y-अक्ष के समानांतर रेखाओं का समीकरण | ||||
| 5 | Introduction to Euclid's Geometry | Point | यूक्लिड की ज्यामिति | बिंदु | |
| Line | रेखा | ||||
| Straight Line | सीधी रेखा | ||||
| Surface | पृष्ठ | ||||
| Plane surface | समतल पृष्ठ | ||||
| Postulate | अभिधारणा | ||||
| Axioms | अभिगृहीत | ||||
| Propositions | साध्य | ||||
| Euclid's Geometry | यूक्लिड की ज्यामिति | ||||
| Euclid's definitions, axioms and postulates | यूक्लिड की परिभाषाएँ, अभिगृहीत और अभिधारणाएँ | ||||
| Equivalent versions of Euclid's fifth postulate | यूक्लिड की पाँचवीं अभिधारणा के समतुल्य रुपान्तरण | ||||
| 6 | Lines and Angles | Line Segment | रेखाएँ और कोण | रेखाखंड | |
| Ray | किरण | ||||
| Collinear Points | संरेख बिंदु | ||||
| Non-collinear Points | असंरेख बिंदु | ||||
| Angle | कोण | ||||
| Arms of the angle | कोण की भुजाएँ | ||||
| Vertex of the angle | कोण का शीर्ष | ||||
| Acute angle | न्यून कोण | ||||
| Right angle | समकोण | ||||
| Obtuse angle | अधिक कोण | ||||
| Straight angle | ऋजु कोण | ||||
| Reflex angle | प्रतिवर्ती कोण | ||||
| Complimentary angles | पूरक कोण | ||||
| Supplementary angles | संपूरक कोण | ||||
| Adjacent angles | आसन्न कोण | ||||
| Linear pair of angles | कोणों का रैखिक युग्म | ||||
| Vertically Opposite Angles | शीर्षाभिमुख कोण | ||||
| Linear pair axiom | रैखिक युग्म अभिगृहीत | ||||
| Transversal | तिर्यक् रेखा | ||||
| Exterior angles | बाह्य कोण | ||||
| Interior angles | अंतः कोण | ||||
| Corresponding angles | संगत कोण | ||||
| Alternate interior angles | एकांतर अंतः कोण | ||||
| Alternate exterior angles | एकांतर बाह्य कोण | ||||
| Consecutive interior angles | क्रमागत अंतः कोण | ||||
| Allied angles | संबंधित कोण | ||||
| Co-interior angles | सह-अंतः कोण | ||||
| Corresponding angles axiom | संगत कोण अभिगृहीत | ||||
| Lines and Angles - Definitions | रेखाएँ और कोण - परिभाषाएँ | ||||
| Intersecting and Non-Intersecting Lines | प्रतिच्छेदी और अप्रतिच्छेदी रेखाएँ | ||||
| Pairs of Angles | कोणों के युग्म | ||||
| Parallel Lines and a Transversal | समानांतर रेखाएँ और तिर्यक रेखा | ||||
| Lines parallel to the same line | एक ही रेखा के समानांतर रेखाएँ | ||||
| Angle sum property of a triangle | त्रिभुज का कोण योग गुण | ||||
| 7 | Triangles | Congruent Figures | त्रिभुज | सर्वांगसम आकृतियाँ | |
| Angle-Side-Angle congruence rule | कोण-भुजा-कोण सर्वांगसमता नियम | ||||
| Angle-Angle-Side congruence rule | कोण-कोण-भुजा सर्वांगसमता नियम | ||||
| Right angle - Hypotenuse - Side congruence rule | समकोण - कर्ण - भुजा सर्वांगसमता का नियम | ||||
| Triangles | त्रिभुज | ||||
| Congruence of Triangles | त्रिभुजों की सर्वांगसमता | ||||
| Criteria for congruence of triangles | त्रिभुजों की सर्वांगसमता के लिए कसौटीयाँ | ||||
| Properties of a Triangle | त्रिभुज के गुण | ||||
| Inequalities in a Triangle | त्रिभुज में असमिकाएँ | ||||
| 8 | Quadrilaterals | Collinear points | चतुर्भुज | संरेख बिंदु | |
| Quadrilaterals | चतुर्भुज | ||||
| Vertices | शीर्ष | ||||
| Trapezium | समलंब | ||||
| Parallelogram | समानांतर चतुर्भुज | ||||
| Rectangle | आयत | ||||
| Rhombus | समचतुर्भुज | ||||
| Square | वर्ग | ||||
| Kite | पतंग | ||||
| Angle Sum Property of a Quadrilateral | चतुर्भुज का कोण योग गुण | ||||
| Types of Quadrilaterals | चतुर्भुज के प्रकार | ||||
| Properties of a Parallelogram | समांतर चतुर्भुज के गुण | ||||
| Condition for a Quadrilateral to be a Parallelogram | चतुर्भुज के समांतर चतुर्भुज होने के लिए प्रतिबन्ध | ||||
| The Mid-point theorem | मध्य-बिंदु प्रमेय | ||||
| 9 | Areas of Parallelograms and Triangles | Planar region | समांतर चतुर्भुजों और त्रिभुजों का क्षेत्रफल | तलीय क्षेत्र | |
| Area | क्षेत्रफल | ||||
| Median of a triangle | त्रिभुज की माध्यिका | ||||
| Figures on the same base and between the same parallels | एक ही आधार पर और एक ही समांतर रेखाओं के बीच आकृतियाँ | ||||
| Parallelograms on the same base and between the same parallels | एक ही आधार और एक ही समांतर रेखाओं के बीच समांतर चतुर्भुज | ||||
| Triangles on the same base and between the same parallels | एक ही आधार और एक ही समांतर रेखाओं के बीच स्थित त्रिभुज | ||||
| 10 | Circles | Radius | वृत्त | त्रिज्या | |
| Centre of a circle | वृत्त का केंद्र | ||||
| Diameter | वृत्त का व्यास | ||||
| Interior of the circle | वृत्त का अभ्यंतर | ||||
| Exterior of the circle | वृत्त का बहिर्भाग | ||||
| Arc | चाप | ||||
| Major arc | दीर्घ चाप | ||||
| Minor arc | लघु चाप | ||||
| Semicircle | अर्धवृत्त | ||||
| Circumference | परिकेन्द्र | ||||
| Segment | वृत्तखंड | ||||
| Major segment | दीर्घ वृत्तखंड | ||||
| Minor segment | लघु वृत्तखंड | ||||
| Sector | त्रिज्यखंड | ||||
| Major sector | दीर्घ त्रिज्यखंड | ||||
| Minor sector | लघु त्रिज्यखंड | ||||
| Chord | जीवा | ||||
| Circumcircle | परिवृत्त | ||||
| Circumcentre | परिकेन्द्र | ||||
| Circumradius | परित्रिज्या | ||||
| Circles | वृत्त | ||||
| Circle - related terms | वृत्त - संबंधित पद | ||||
| Angle subtended by a chord at a point | जीवा द्वारा एक बिंदु पर अंतरित कोण | ||||
| Perpendicular from the centre to a chord | केंद्र से जीवा पर लंब | ||||
| Circle through three points | तीन बिंदुओं से जाने वाला वृत्त | ||||
| Equal chords and their distances from the centre | समान जीवाएं और उनकी केंद्र से दूरीयाँ | ||||
| Angle subtended by an arc of a circle | एक वृत्त के चाप द्वारा अंतरित कोण | ||||
| Cyclic Quadrilaterals | चक्रीय चतुर्भुज | ||||
| 11 | Constructions | Basic constructions | रचनाएँ | आधारभूत रचनाएँ | |
| Constructions of triangles | त्रिभुजों की रचनाएँ | ||||
| 12 | Heron's formula | Equilateral triangle | हीरोन का सूत्र | समबाहु त्रिभुज | |
| Heron's formula | हीरोन का सूत्र | ||||
| Area of Triangle - by Heron's formula | त्रिभुज का क्षेत्रफल - हीरोन के सूत्र द्वारा | ||||
| Applications of Heron's formula in finding areas of quadrilaterals | चतुर्भुजों का क्षेत्रफल ज्ञात करने में हीरोन के सूत्र का अनुप्रयोग | ||||
| 13 | Surface Area and Volumes | Plane figures | पृष्ठीय क्षेत्रफल और आयतन | समतल आकृतियाँ | |
| Solid figures | ठोस आकृतियाँ | ||||
| Cuboid | घनाभ | ||||
| Cube | घन | ||||
| Surface area | पृष्ठीय क्षेत्रफल | ||||
| Volume | आयतन | ||||
| Cylinder | बेलन | ||||
| Prisms | प्रिज्म | ||||
| Pyramids | पिरामिड | ||||
| Cone | शंकु | ||||
| Sphere | गोला | ||||
| Hemisphere | अर्धगोला | ||||
| Curved surface area | वक्र पृष्ठ का क्षेत्रफल | ||||
| Total surface area | कुल पृष्ठीय क्षेत्रफल | ||||
| Surface Area and Volumes | पृष्ठीय क्षेत्रफल और आयतन | ||||
| Surface Area of a Cuboid and a Cube | घनाभ और घन के पृष्ठीय क्षेत्रफल | ||||
| Surface Area of a right circular cylinder | एक लम्ब वृत्तीय बेलन का पृष्ठीय क्षेत्रफल | ||||
| Surface Area of a right circular cone | एक लम्ब वृत्तीय शंकु का पृष्ठीय क्षेत्रफल | ||||
| Surface area of a sphere | गोले का पृष्ठीय क्षेत्रफल | ||||
| Volume of a cuboid | घनाभ का आयतन | ||||
| Volume of a cylinder | बेलन का आयतन | ||||
| Volume of a right circular cone | लम्ब वृत्तीय शंकु का आयतन | ||||
| Volume of a sphere | गोले का आयतन | ||||
| 14 | Statistics | Data | सांख्यिकी | आंकड़े | |
| Statistics | सांख्यिकी | ||||
| Primary data | प्राथमिक आंकड़े | ||||
| Secondary data | गौण आंकड़े | ||||
| Raw data | यथाप्राप्त आंकड़े | ||||
| frequency distribution table | बारंबारता बंटन सारणी | ||||
| Tally marks | मिलान चिन्ह | ||||
| Class-interval | वर्ग-अंतराल | ||||
| Class-size | वर्ग-माप | ||||
| Class Limit | वर्ग-सीमा | ||||
| Lower Class Limit | निम्न वर्ग-सीमा | ||||
| Upper Class Limit | उपरि वर्ग-सीमा | ||||
| Bar graphs | दंड आलेख | ||||
| Histogram | आयतचित्र | ||||
| Frequency polygon | बारंबारता बहुभुज | ||||
| Central Tendency | केंद्रीय प्रवृत्ति | ||||
| Collection of data | आँकड़ों का संग्रह | ||||
| Presentation of data | आंकड़ों का प्रस्तुतिकरण | ||||
| Graphical representation of data | आंकड़ों का आलेखीय निरूपण | ||||
| Measures of central tendency | केंद्रीय प्रवृत्ति के माप | ||||
| 15 | Probability | Probability | प्रायिकता | प्रायिकता | |
| Empirical Probability | आनुभविक प्रायिकता | ||||
| Event (Probability) | घटना(प्रायिकता) | ||||
| Probability - an experimental approach | प्रायिकता-एक प्रायोगिक दृष्टिकोण | ||||
| 16 | Proofs in Mathematics | Deductive Reasoning | गणित में उपपत्तियाँ | निगमनिक तर्कण | |
| Axioms | अभिगृहीत | ||||
| Mathematically acceptable statements | गणितीय रूप से स्वीकार्य कथन | ||||
| Theorems, conjectures and axioms | प्रमेय, कंजेक्चर,और अभिगृहीत | ||||
| What is a Mathematical Proof | गणितीय उपपत्ति क्या है? | ||||
| Conjecture | अनुमान(कंजेक्चर) | ||||
| Theorem | प्रमेय | ||||
| Hypothesis | परिकल्पना | ||||
| 17 | Mathematical Modelling | Mathematical Modelling | गणितीय निदर्शन | गणितीय निदर्शन | |
| Formualtion | सूत्रण | ||||
| Solution | हल | ||||
| Interpretation | निर्वचन | ||||
| Validation | मान्यकरण | ||||
| Problem statement | समस्या कथन | ||||
| Mathematical description | गणितीय वर्णन | ||||
| Mathematical Models | गणितीय निदर्श | ||||
| The Process of Modelling, its advantages and limitations | निदर्शन प्रक्रम, इसके लाभ और सीमाएँ |
