Question

if two lines intersect ea h other prove that their. vertically opposite angles are equal
please give answer please today is my test in 10 mins please give​

Answer 1

Proof :-

In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O .They lead to two pairs of vertically opposite angles, namely,

(i) ∠ AOC and ∠ BOD  (ii) ∠ AOD and ∠ BOC.

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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