Chapter 12, Problem 1CT

To determine

To Proof: The expression $\Delta ABC\cong \Delta EDC$ .

Answer to Problem 1CT

The two sides are congruent so the triangle is isosceles.

Explanation of Solution

Given Data:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

The objective is to determine that $\Delta ABC\cong \Delta EDC$ .

Consider the relation between the side is,

  $\begin{array}{c}\overline{CA}\cong \overline{CB}\\ \cong \overline{CD}\\ \cong \overline{CE}\end{array}$

By the vertical angle congruence theorem is,

  $\angle ACB\cong \angle ECD$

Then, by the congruence theorem,

  $\Delta ABC\cong \Delta EDC$

Hence, proved.