Question

In the given figure, $ABC$ is an isosceles triangle in which $AB=AD$. Also, $D$ is a point such that $BD=CD$. then "$AD$ bisects $\angle A$ and $\angle D$." is ?

• A. True
• B. False

Answer 1

The correct option is A True

Given :

$△ABC$ is an isosceles triangle.

$AB=AC$

$BD=CB$

To prove :

$AD$ bisects $\angle A$ and $\angle D$

Proof :

Consider $△ABD$ and $△ACD$

$\Rightarrow$ $AB=AC$ [ Given ]

$\Rightarrow$ $BD=CD$ [ Given ]

$\Rightarrow$ $AD=AD$ [ Common side ]

$\therefore$ $△ABD\cong △ACD$ [ By $SSS$ congruence property ]

$\Rightarrow$ $\angle BAD=\angle CAD$ [ C.P.C.T ]

$\Rightarrow$ $\angle BDA=\angle CDA$ [ C.P.CT. ]

Hence, we have proved that $AD$ bisects $\angle A$ and $\angle D.$