Question

how to prove vertically opposite angles are equal ?​

Answer 1

Answer:

If two lines intersect each other, then the vertically opposite angles are equal.

Proof :

If two lines intersect each other, then the vertically opposite angles are equal.

In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O

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

Answer 2

Vertically opposite angles are equal