Chapter 4, Problem 20RP

To determine

To Verify: $CD=DE.$

Explanation of Solution

Given information: $AB=AF,BC=FE$

Formula Used: Congruency of triangle.

Proof:

  $\begin{array}{l}AB=AF\text{ and }BC=FE \left(\text{given}\right)\\ \angle BAE=\angle FAC\left(\text{Common angle}\right)\\ \therefore AC=AE\\ \therefore \Delta BAE\cong \Delta FAC\text{(SAS)}\\ \therefore \angle BCD=\angle FED\text{(CPCT})\\ \angle BDC=\angle FDE\left(\text{Vertically opposite angle}\right)\\ \Delta BDC\cong \Delta FDE\text{(AAS)}\\ CD=DE\text{(CPCT)}\end{array}$