Question

5. Prove that if two straight lines cut one another, the vertically opposite angles are equal.

Answer 1

Answer:

Take two lines AB and CD which intersect each other at a point O.

∠AOC + ∠AOD = 180° (Linear Pair)

∠COB + ∠AOC = 180° (Linear Pair)

Equating the two,

∠AOC + ∠AOD = ∠BOC + ∠AOD

Removing ∠AOD from both sides,

∠AOC = ∠BOC

Hence Proved