- Books Name
- class 7 Mathematics Book
- Publication
- ReginaTagebücher
- Course
- CBSE Class 7
- Subject
- Mathmatics
Angles on a straight line, intersecting lines
Complementary Angle: The sum of the measures of two angles is 90°
Supplementary Angle: The sum of the measures of two angles is 180°
Adjacent Angle: Adjacent angles have a common vertex and a common arm but no common interior points
Linear pair: A linear pair is a pair of adjacent angles whose non-common sides are opposite rays
Vertically Opposite Angles: when two lines intersect, the vertically opposite angles so formed are equal Pairs of Lines
Intersecting lines: Two lines intersect if they have a point in common. This common point O is their point of intersection.
Adjacent Angles
A pair of angles which are placed next to each other in such a way that they have a common vertex and an arm which is common to both the angles are called adjacent angles.
Linear Pair
A linear pair is a pair of adjacent angles whose non-common arms are opposite rays.
A pair of angles placed adjacent to each other is called a linear pair if the sum of their measures is 180°.
Note: A pair of supplementary angles form a linear pair when placed adjacent to each other.
When two lines intersect, the vertically opposite angles so formed are equal.
∠1 + ∠2 = 180° …(1)
∵ ∠1 and ∠2 form a linear pair
∠3 + ∠2 = 180° …(2)
∵ ∠3 and ∠2 form a linear pair
From (1) and (2)
∠1 = ∠3
Similarly, we can prove that ∠2 = ∠4
Intersecting Lines
Two lines intersect if they have a point in common called their point of intersection.