Chapter 4.4, Problem 12PSB

To determine

To Verify: $AD=DC$

Explanation of Solution

Given information: $AB=BC;AE=EC\text{.}$ .

Formula used: congruency of triangles

Proof:

  $\begin{array}{l}AB=BC;AE=EC\text{.}(\text{given})\\ BE=BE(\text{Reflective}\text{property)}\\ \therefore \Delta ABE\cong \Delta CBE(\text{SSS})\\ \therefore \angle ABD=\angle CBD(\text{CPCT})\\ BD=BD(\text{Reflective}\text{property)}\\ \therefore \Delta ABD\cong \Delta CBD(\text{SAS})\\ \therefore AD=DC(CPCT)\end{array}$