Question

prove that if two lines intersect each other then vertically opposite angle are equal

Answer 1

Prove that if two lines are intersecting, then thevertically opposite angles are equal. Given two lines AB and CD intersect each other at the point O. Given two lines AB and CD intersect each otherat the point O.

Answer 2

Given :- Two lines intersect at point O

To Prove :- vertically opposite angles are equal

                    i.e ∠AOC = ∠BOD

                    and ∠AOD = ∠BOC

Proof :- on line AB

              ∠AOC+∠BOC = 180° ··········(1)      (linear pair)

             on line CD

               ∠AOD+∠AOC = 180° ..........(2)      (linear pair)

from (1) and (2)

         ∠AOC+∠BOC = ∠AOD+∠AOC

                      ∠BOC = ∠AOD

Similarly we can prove that ∠BOD = ∠AOC

    Hence vertically opposite angles are equal