Question

Prove that if two lines intersect each other,then the vertically opposite angles are equal

Answer 1

In the figure given above, the line segment AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ meet at the point O and these represent two intersecting lines. The line segment PQ¯¯¯¯¯¯¯¯ and RS¯¯¯¯¯¯¯ represent two parallel lines as they have no common intersection point in the given plane. Infinite lines can pass through a single point and hence through O, multiple intersecting lines can be drawn. Similarly, infinite parallel lines can be drawn parallel to PQ¯¯¯¯¯¯¯¯ and RS¯¯¯¯¯¯¯ . Also, it is worth noting that the perpendicular distance between two parallel lines is constant.

In a pair of intersecting lines, the angles which are opposite to each other form a pair of vertically opposite angles. In the figure given above, ∠AOD and ∠COB form a pair of vertically opposite angle and similarly ∠AOC and ∠BOD form such a pair. These angles are also known as vertical angles or opposite angles.

For a pair of opposite angles the following theorem, known as vertical angle theorem holds true:

Theorem: In a pair of intersecting lines the vertically opposite angles are equal.

Answer 2

Step-by-step explanation:

see the answer it is attached