# Lines and Angles Class 7 Notes: Chapter 5

## Introduction to Geometry

#### For More Information On Introduction To Geometry, Watch The Below Video.

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### Line, line segment and ray

• If we take a point and draw a straight path that extends endlessly on both the sides, then the straight path is called as a line.
• A ray is a part of a line with one endpoint.
• A line segment is a part of a line with two endpoints.

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### Angles

• An angle is formed when two rays originate from the same end point.
• The rays making an angle are called the arms of the angle.
• The end point is called the vertex of the angle.

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### Complementary Angles

• Two angles whose sum is 900 are called complementary angles.
Example: 500Â + 400Â = 900
âˆ´Â 500 and 400 angles are complementary angles.

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## Parallel Lines and a Transversal

### Transversal intersecting two lines

• Transversal is a line that intersects two or more lines at different points.

• Corresponding Angles:
(i) âˆ 1 and âˆ 5 (ii) âˆ 2 and âˆ 6
(iii) âˆ 3 and âˆ 7 (iv) âˆ 4 and âˆ 8
• Alternate Interior Angles:
(i) âˆ 3 and âˆ 6 (ii) âˆ 4 and âˆ 5
• Alternate Exterior Angles:
(i) âˆ 1 and âˆ 8 (ii) âˆ 2 and âˆ 7
• Interior angles on the same side of the transversal:
(i) âˆ 3 and âˆ 5 (ii) âˆ 4 and âˆ 6

### Transversal of Parallel Lines

• If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(i) âˆ 1=âˆ 5 (ii) âˆ 2=âˆ 6
(iii) âˆ 3=âˆ 7 (iv) âˆ 4=âˆ 8
• If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
(i) âˆ 3=âˆ 6 (ii) âˆ 4=âˆ 5
• If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
(i) âˆ 3+âˆ 5=1800 (ii) âˆ 4+âˆ 6=1800

### Checking if two or more lines are parallel

• There are three conditions to check whether the two lines are parallel. They are:
(i)Â If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
(ii)Â If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
(iii)Â If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

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## Intersecting Lines and Pairs of Angles

### Supplementary angles

• Two angles whose sum is 1800 are called supplementary angles.
Example:Â 1100+700=900
âˆ´Â 1100 and 700 angles are supplementary angles.

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• Two angles are adjacent, if they have
(i) A common vertex
(ii) A common arm
(iii) Their non-common armsÂ on different sides of the common arm.

Here âˆ ABD and âˆ DBCÂ are adjacent angles.

### Linear Pair

• Linear pair of angles are adjacent angles whose sumÂ is equal to 180âˆ˜.

Here, 1 and 2 are linear pair of angles.

### Vertically Opposite Angles

• Vertically opposite angles are formed when two straight lines intersect each other at a common point.
• Vertically opposite angles are equal.

Here, the following pairs of angles are vertically opposite angles.
(i) a and c
(ii) b and d

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### Intersecting and Non-Intersecting lines

• Intersecting lines areÂ lines whichÂ intersect at a common point called the point of intersection.
• Parallel lines areÂ lines which do not intersect at any point. Parallel lines are also known as non- intersecting lines.

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## Basic Properties of a Triangle

### Sum of Interior Angles in a Triangle

• Angle sum property of a triangle: Sum of all interior angles of a triangle is 1800.

In â–³ABC, âˆ 1+âˆ 2+âˆ 3=1800

### The exterior angle of a triangle = Sum of opposite internal angles

• If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

In â–³ABC, âˆ CAB+âˆ ABC=âˆ ACD.

#### For More Information On Exterior Angle Theorem, Watch The Below Video.

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## Frequently asked Questions on CBSE Class 7 Maths Notes Chapter 5: Lines and Angles

### What is the definition of a â€˜Rayâ€™?

In geometry, a ray is usually taken as a half-infinite line with one of the two points and. taken to be at infinity.