Question

if two lines intersect each other then prove that the verically opposite angles are equal​

Answer 1

Step-by-step explanation:

let AB and CD be two lines intersecting at O as shown in Fig. 6.8. 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

Answer 2

Given:-AB and CD two lines intersect each other at the point o. Then angle boc,angle aod ; and angle Aoc ,angle Bod are vertically opposite angle.

To prove:-angle boc =angle aod

and angle Aoc=angle Bod

proof:-oc ray stands on AB line

therefore,angle Aoc +angle boc =180°

ob Ray stands on CD line

therefore,angle boc+angle Bod =180°

therefore,angle Aoc+angle Boc=angle Boc+angle Bod

therefore, angle Aoc=angle Bod

similarly angle Boc =angle Aod