Theorem 6.1 : If two lines intersect each other, then the vertically opposite angles are equal.
Given: Two lines AB and CD are interested at point O.
To Prove: (i) ∠AOC = ∠BOD
(ii) ∠AOD = ∠BOC
Proof: Now, ray OA stands on line CD.
Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………… (1)
Can we write ∠ AOD + ∠ BOD = (Linear pair axiom) …………(2)
From (1) and (2), we can write
∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD
This implies that ∠ AOC = ∠ BOD
Similarly, it can be proved that ∠AOD = ∠BOC