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.

Question

Philoid · Accepted Answer

Given that,

AB and CD are two lines intersecting at O

To prove: ∠BOC = 90^o

∠AOC = 90^o

∠AOD = 90^o

∠BOD = 90^o

Proof: Given that,

∠BOC = 90^o

∠BOC = ∠AOD = 90^o(Vertically opposite angle)

∠AOC + ∠BOC = 180^o(Linear pair)

∠AOC + 90^o = 180^o

∠AOC = 90^o

∠AOC = ∠BOD = 90^o(Vertically opposite angles)

Therefore,

∠AOC = ∠BOC = ∠BOD = ∠AOD = 90^o

Hence, proved