Question

In the given $\Delta$ $ABC$, if $AB$ $=$ $AC$ and $BD$ $=$ $DC$, then $\angle$ $ADC$ $=$ ___________.

• A. ${60}^o$
• B. ${120}^o$
• C. ${90}^o$
• D. ${45}^o$

Answer 1

The correct option is C ${90}^o$

Considering the triangles $\Delta ABD$ and $\Delta ACD$

$AB=AC$ ....Given

$BD=DC$ .....Given

$AD=AD$ ....Common

So, by $SSS$ congruency

$\Delta ABD$ $\cong$ $\Delta ACD$

Corresponding sides and angles of congruent triangles are also equal

$\Rightarrow \angle ADC=\angle ADB$

We know that $BDC$ is a straight line

$\angle ADC+\angle ADB={180}^{\circ }$

$\Rightarrow 2\angle ADC={180}^{\circ }$

$\Rightarrow \angle ADC={90}^{\circ }$