Question

If ray OC stands on a line AB such that AOC = BOC (Fig), then show that AOC = 90°.​

Answer 1

Given :

Given that, ray OC stands on the line AB such that ∠AOC = ∠BOC.

To prove :

We'll have to prove that ∠AOC = 90°.

Proof :

The ray OC stands on AB such that :

➻ ∠AOC = ∠BOC . . . . . ( eqⁿ . ⓵ )

According to the linear pair axiom,

If a ray stands on a line, then the sum of adjacent angles is 180°.

So :

➻ ∠AOC + ∠BOC = 180°

From eqⁿ . ⓵ :

➻ ∠AOC + ∠AOC = 180°

➻ 2 ∠AOC = 180°

➻ ∠AOC = 180°/2

➻ ∠AOC = 90°

Therefore, proved!