Chapter 6, Problem 13CR

Solution

To Prove: The congruency of $\angle B$ with respect to $\angle C$

Given information: $\overline{AB}\cong \overline{AC}$ and $\overline{BD}\cong \overline{DC}$ is provided in the question which will help to find the solution.

  

Proof: Here, we have been joined AD

In $\Delta ADB$ and $\Delta ADC$ ,

AB = AC (given)

And, BD = DC (given)

And, AD = AD (common)

Hence, $\Delta ADB\cong \Delta ADC$ (by side, side, side congruency rule)

So that, $\angle B\cong \angle C$ (by corresponding parts of congruent triangles)