प्रतिच्छेदी और अप्रतिच्छेदी रेखाएँ: Difference between revisions

Revision as of 08:11, 24 June 2024

प्रतिच्छेदी रेखाएँ वे रेखाएँ होती हैं जो किसी समतल में एक दूसरे से मिलती हैं या एक दूसरे को काटती हैं। जब दो या दो से अधिक रेखाएँ किसी भी बिंदु पर नहीं मिलती हैं, तो उन्हें अप्रतिच्छेदी रेखाएँ कहा जाता है।

प्रतिच्छेदी रेखाएँ

When two or more lines meet at a common point, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection. Observe the following figure which shows two intersecting lines $AB$ and $CD$ and the point of intersection $O$ .

चित्र-1 प्रतिच्छेदी रेखाएँ

प्रतिच्छेदित रेखाओं के गुण

Intersecting lines meet at a single point, they cannot meet at more than one point.
Intersecting lines meet each other at any angle which is greater than $0^{\circ }$ and less than $180^{\circ }$ .

अप्रतिच्छेदी रेखाएँ

When two or more lines do not intersect with each other, they are termed as non-intersecting lines. Observe the following figure of two non-intersecting, parallel lines $PQ$ and $RS$ .

चित्र-2 अप्रतिच्छेदी रेखाएँ

अप्रतिच्छेदित रेखाओं के गुण

Non-intersecting lines never meet and do not share any common point. They are also known as parallel lines.
The distance between non-intersecting lines is always the same.

@@ Line 1: / Line 1: @@
-Intersecting lines are those lines that meet or cross each other in a plane. When two or more lines do not meet at any point, they are called non-intersecting lines.
+प्रतिच्छेदी रेखाएँ वे रेखाएँ होती हैं जो किसी समतल में एक दूसरे से मिलती हैं या एक दूसरे को काटती हैं। जब दो या दो से अधिक रेखाएँ किसी भी बिंदु पर नहीं मिलती हैं, तो उन्हें अप्रतिच्छेदी रेखाएँ कहा जाता है।
-== Intersecting lines ==
+== प्रतिच्छेदी रेखाएँ ==
 When two or more lines meet at a common point, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection. Observe the following figure which shows two intersecting lines <math>AB</math> and <math>CD</math> and the point of intersection <math>O</math>.
-[[File:Intersecting lines.jpg|alt=Fig. 1 - Intersecting lines|none|thumb|Fig. 1 - Intersecting lines]]
+[[File:Intersecting lines.jpg|alt=Fig. 1 - Intersecting lines|none|thumb|चित्र-1 प्रतिच्छेदी रेखाएँ]]
-== Properties of Intersecting Lines ==
+== प्रतिच्छेदित रेखाओं के गुण ==
 * Intersecting lines meet at a single point, they cannot meet at more than one point.
 * Intersecting lines meet each other at any angle which is greater than <math>0^\circ</math> and less than <math>180^\circ</math>.
-== Non-Intersecting lines ==
+== अप्रतिच्छेदी रेखाएँ ==
-When two or more lines do not intersect with each other, they are termed as non-intersecting lines. Observe the following figure of two non-intersecting, parallel lines <math>PQ</math> and <math>RS</math>.[[File:Non-Intersecting lines.jpg|alt=Fig. 2 - Non intersecting lines|none|thumb|Fig. 2 - Non intersecting lines]]
+When two or more lines do not intersect with each other, they are termed as non-intersecting lines. Observe the following figure of two non-intersecting, parallel lines <math>PQ</math> and <math>RS</math>.[[File:Non-Intersecting lines.jpg|alt=Fig. 2 - Non intersecting lines|none|thumb|चित्र-2  अप्रतिच्छेदी रेखाएँ]]
-== Properties of Non-intersecting Lines ==
+== अप्रतिच्छेदित रेखाओं के गुण ==
 * Non-intersecting lines never meet and do not share any common point. They are also known as parallel lines.