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.
Solution:
Given,
AB and CD are two lines intersecting at O, such that
∠BOC = 90, ∠AOC = 90 ∠AOD = 90° and ∠BOD = 90
Proof:
Given that B0C = 90
Vertically opposite angles are equal
BOC = AOD = 90
A0C, BOC are a Linear pair of angles
∠AOC + ∠BOC = 180°
[Linear pair]
AOC + 90 = 180
AOC = 90
Vertically opposite angles
Therefore, AOC = BOD = 90
Hence, AOC = BOC = BOD = AOD = 90