Question

observe the adjacent figure. write 'given and 'to prove for the theorem 'the opposite angles formed by two intersecting lines are of equal measures'

Answer 1

✪ Given : AB and CD are two straight lines.

✪ To prove :∠AOD = ∠BOC and ∠AOC = ∠BOD

✪ Proof : Since ∠AOC and ∠AOD for linear pair.

∠AOC + ∠AOD = 180° _(i)

Since ∠AOC and ∠BOC form linear pair.

∠AOC + ∠BOC = 180° _(ii)

From (i) and (ii) equations we get,

∠AOC + ∠AOD = ∠AOC + ∠BOC

∠AOD = ∠BOC

Similarly we will prove, ∠AOC = ∠BOD

✪ Q.E.D