Chapter 3.3, Problem 1PSA

To determine

To show that two angles are congruent.

Answer to Problem 1PSA

  $\angle Aand\angle Darecongruent.$

Explanation of Solution

Given information:

  $\begin{array}{l}\overline{AB } \cong \overline{DE}\hfill \\ \overline{BC} \cong \overline{EF}\hfill \\ \overline{AC} \cong \overline{DF}\hfill \end{array}$

Formula used:

The below property is used:

Two triangles are congruent by SSS congruence rule.

Proof:

From figure,we get

  

It is given that,

  $\begin{array}{l} \overline{AB } \cong \overline{DE}\hfill \\ \overline{BC} \cong \overline{EF}\hfill \\ \overline{AC} \cong \overline{DF}\hfill \end{array}$

By SSS congruence rule, we get

  $\Delta ABC \cong \Delta DEF$

As corresponding parts of congruent triangles are congruent, we get

  $\angle A \cong \angle D$