If one of the four angles formed by two intersecting lines is a right

1.	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» Given that, AB and CD are two lines intersecting at O To prove: ∠BOC = 90° ∠AOC = 90° ∠AOD = 90° ∠BOD = 90° Proof: Given that, ∠BOC = 90° ∠BOC = ∠AOD = 90°(Vertically opposite angle) ∠AOC + ∠BOC = 180°(Linear pair) ∠AOC + 90° = 180° ∠AOC = 90° ∠AOC = ∠BOD = 90°(Vertically opposite angles) Therefore, ∠AOC = ∠BOC = ∠BOD = ∠AOD = 90° Hence, proved

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»

Given that,

AB and CD are two lines intersecting at O

To prove:

∠BOC = 90°

∠AOC = 90°

∠AOD = 90°

∠BOD = 90°

Proof: Given that,

∠BOC = 90°

∠BOC = ∠AOD = 90°(Vertically opposite angle)

∠AOC + ∠BOC = 180°(Linear pair)

∠AOC + 90° = 180°

∠AOC = 90°

∠AOC = ∠BOD = 90°(Vertically opposite angles)

Therefore,

∠AOC = ∠BOC = ∠BOD = ∠AOD = 90°

Hence, proved