Chapter 3.3, Problem 5PSA

To determine

To show that two sides are congruent.

Answer to Problem 5PSA

  $\overline{AB}and\overline{YZ}arecongruent.$

Explanation of Solution

Given information:

  $\begin{array}{l}\angle B \cong \angle Y\hfill \\ Cismidpointof\overline{BY.}\hfill \end{array}$

Formula used:

The below properties are used:

A midpoint divides a segment into two equal congruent segments.

Vertical angles are congruent.

Two triangles are congruent by ASA congruence rule.

Proof:

It is given that,

  $\begin{array}{l}\angle B \cong \angle Y\hfill \\ Cismidpointof\overline{BY.}\hfill \end{array}$

  

A midpoint divides a segment into two equal congruent segments.

  $\overline{BC} \cong \overline{CY}$

Vertical angles are congruent.

  $\angle 1 \cong \angle 2$

By ASA congruence rule, we get

  $\Delta ABC \cong \Delta ZYC$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{AB} \cong \overline{ZY}$