Chapter 10.6, Problem 2PSA

To determine

Give the explanation for the given proof.

Explanation of Solution

Given:

The given diagram is

  

$AC$ is the diameter and $\overline{BC}\cong \overline{CD}$ . Show that $\Delta ABC\cong \Delta ADC$ .

Calculation:

Use theory, the angle inscribed in a semi-circle is a right angle.

  $\angle ABC=\angle ADC={90}^{°}$ .

In $\Delta ABC$ and $\Delta ADC$ .

  $\overline{BC}\cong \overline{CD}$ (given)

  $\angle ABC\cong \angle ADC$

  $\overline{AC}\cong \overline{AC}$ (from figure)

From right angle congruency theorem, the hypotenuse $\left(\overline{AC}\cong \overline{AC}\right)$ and the corresponding bases $\left(\overline{BC}\cong \overline{CD}\right)$ are equal.

Hence the $\Delta ABC\cong \Delta ADC$ .