Question

If one of the four angles formed by two intersecting lines is a right angle, then show that
each of the four angles is a right angle.

Answer 1

Given,

AB and CD are two lines intersecting at O such that

`∠`BOC = 90°

`∠`AOC = 90°, `∠`AOD = 90° and `∠`BOD = 90°

Proof:

Given that `∠`BOC = 90°

Vertically opposite angles are equal

`∠`BOC = `∠`AOD = 90°

`∠`AOC, `∠`BOC are Linear pair of angles

`∠`AOC + `∠`BOC = 180°       [LinearPair]

⇒`∠`AOC + 90° = 180°

⇒ `∠`AOC = 90°

Vertically opposite angles

∴ `∠`AOC = `∠`BOD = 90°

Hence, `∠`AOC = `∠`BOC = `∠`BOD = `∠`AOD = 90°