Question

Question 15
In the given figure, $\angle BAC$=${90}^{\circ }$ and AD $\perp$ BC.

The number of right-angled triangles in the figure is

a) 1
b) 2
c) 3
d) 4

Answer 1

A triangle, in which one angle is equal to ${90}^{\circ }$, is called a right-angled triangle.

In the above figure, $\Delta ABC$ is a right angle triangle.

In the above figure,

Given : $\angle BAC$=${90}^{\circ }$ and AD $\perp$ BC

Since, $\angle BAC={90}^{\circ }$

$\therefore △BAC$ is a right angled triangle.

Also, $\angle ADB=\angle ADC$ = ${90}^{\circ }$ $[\therefore AD\perp BC]$.

$△ADB$ and $△ADC$ are also right angled triangles.

Hence, there are 3 right-angled triangles $△BAC$, $△ADB$ and $△ADC$ .