Chapter 6, Problem 10RP

Solution

To Prove: $\Delta BAC$ is isosceles

Given information: $\Delta BDC$ is isosceles, with $\overline{BD}\cong \overline{CD}$ and $\angle ADB\cong \angle ADC$ is provided in the question which will help to find the solution.

Proof: $\Delta BDC$ is isosceles,

So, BD = CD

  $\angle ADB\cong \angle ADC$ (given)

And, $\angle CBD=\angle DCB$ (angle opposite to equal sides are equal)

And, as $\angle AOB=\angle AOC$

So that, AB = AC (sides opposite to equal angles are equal)

Hence, we can say that

  $\Delta BAC$ is isosceles.