Question

If two lines intersect with each other then prove that they are vertically opposite angles. With diagram.​

Answer 1

Answer:

In the statement above, it is given that ‘two lines intersect each other’. So, 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.

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

• Can we write ∠ AOD + ∠ BOD = 180°? (Linear pair axiom)……………(2)

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

• ∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

• This implies that ∠ AOC = ∠ BOD

• Similarly, it can be proved that ∠AOD = ∠BOC