Chapter 6, Problem 4PT

To determine

The angle that is congruent to angle C.

Answer to Problem 4PT

The angle congruent to $\angle BCD$ is $\angle ADC$ .

Explanation of Solution

Given:

ABCD is an isosceles triangle.

Calculation:

According to the definition of an isosceles trapezoid,

  $\overline{AD}\cong \overline{BC.}$

In an isosceles trapezoid, every pair of base angles is congruent.

Therefore,

  $\angle ADC\cong \angle BCD.$

Thus, the angle congruent to $\angle BCD$ is $\angle ADC$ .