Question

Question 44

If D is the mid-point of side BC in $\Delta ABC$, where AB = AC, then $\angle ADC$ is

a) ${60}^{\circ }$
b) ${45}^{\circ }$
c) ${120}^{\circ }$
d) ${90}^{\circ }$

Answer 1

In $\Delta ADB$ and $\Delta ADC$,
BD = DC [D is the mid-point]
AB = AC [given]
AD = AD [common side]

By SSS congruence criterion, $\Delta ABD\cong \Delta ACD$
$\therefore \angle ADB=\angle ADC$ [by CPCT]
We know that, $\angle ADB+\angle ADC={180}^{\circ }$ [linear pair]
$\Rightarrow 2\angle ADC={180}^{\circ }$ [$\because \angle ADB=\angle ADC$]
$\Rightarrow \angle ADC={90}^{\circ }$
Hence option (d) is correct.