Question

theorem 6.1 for class 9- if two lines intersect each other then the vertically opposite angles are equal​

Answer 1

Answer:

yes these are equal because ,

by angle sum property

(angles of a triangle is equal to 180°

Answer 2

Proof of two lines intersect each other then the vertically opposite angles are equal​

Step-by-step explanation:

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)

We can write ∠ AOD + ∠ BOD = 180°  (Linear pair axiom)……………(2)

From (1) and (2), we can write

∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

This implies that ∠ AOC = ∠ BOD  

Therefore it is proved lines intersect each other then the vertically opposite angles are equal​.