Question

Prove: - The opposite angles formed by 2 intersecting lines are of equal measures

Answer 1

Step-by-step explanation:

We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.

Now, ray OA stands on line CD.

Therefore, ∠ AOC + ∠ AOD = 180°  (Linear pair axiom) ………..(1)

Can we write ∠ AOD + ∠ BOD = 180°?  (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

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