Question

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

Answer 1

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