Question

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

Answer 1

Given Two lines AB and CD intersect each other at O. $\angle AOC={90}^0$
To prove: $\angle AOD=\angle BOC=\angle BOD={90}^0$
Proof: $\because$ AB and CD intersect each other at O
$\therefore \angle AOC=\angle BODand\angle BOC=\angle AOD$
(Vertically opposite angles)
But $\angle AOC={90}^0$
$\therefore \angle BOD={90}^0$
$\therefore \angle AOC+\angle BOC={180}^0$ (Linear pair)
$\Rightarrow {90}^0+\angle BOC={180}^0\therefore \angle BOC={180}^0-{90}^0={90}^0\therefore \angle AOD=\angle BOC={90}^0\therefore \angle AOD=\angle BOC=\angle BOD={90}^0$