Chapter 7.2, Problem 61SPR

To determine

To Proof: The triangle ABCE is an isosceles trapezoid.

Explanation of Solution

Given:

The midpoints are E and C of $AD$ and $DB$ . Also $\overline{AD}\cong \overline{DB}$ , $\angle A\cong \angle 1$ .

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Since, $\angle A\cong \angle 1$ then by the converse of the postulate shows that $\overline{AD}=\overline{DB}$ with the mid points E and C.

Then, by the midpoint theorem.

  $\begin{array}{l}AE=\frac{1}{2}AD\\ BC=\frac{1}{2}BD\end{array}$

Then,

  $AE=BC$

Thus, by the definition of the congruence $\overline{AE}\cong \overline{BC}$ and ABCE is an isosceles trapezoid.

Hence, proved.