Chapter 5, Problem 20CUR

To determine

To complete: the given statement about the diagram.

Answer to Problem 20CUR

  $\Delta ADC$ is an isosceles triangle.

Explanation of Solution

Given information:

Given figure,

  

Given:

  $ABCD$ is a parallelogram;

  $\overline{AD}\cong \overline{AC}$ ; $\overline{AE}\cong \overline{EC}$

  $\angle ADF\cong \angle CDF$ ; $m\angle DAC=36$ .

Given statement,

  $\Delta ADC$ is a ----triangle.

Calculation:

Look at the parallelogram $ABCD$ , and see that $\overline{AD}\cong \overline{AC}$ in $\Delta ADC$ .

As isosceles triangle is a triangle with two congruent sides, the congruent sides are called legs and third side called base.

Hence in $\Delta ADC$ , as $\overline{AD}\cong \overline{AC}$

Hence, these two sides are legs and segment $\overline{DC}$ is a base of $\Delta ADC$ .

Thus, $\Delta ADC$ is an isosceles triangle.