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.

Given:

One of the four angles formed by two intersecting lines is a right angle.

To do:

We have to show that each of the four angles is a right angle.

Solution:

Let two lines $AB$ and $CD$ intersect each other at $O$ such that $\angle AOC=90^o$.

We know that,

Vertically opposite angles are equal.

Therefore,

$\angle BOD = \angle AOC = 90^o$ and $\angle BOC = \angle AOD$ (Vertically opposite angles)

$\angle AOC + \angle BOC = 180^o$              (Linear pair)

$90^o + \angle BOC = 180^o$

$\angle BOC = 180^o - 90^o = 90^o$

$\angle AOD = \angle BOC = 90^o$

This implies each of the four angles is a right angle

Hence proved.

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Updated on: 10-Oct-2022

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