Chapter 3.2, Problem 28PSC

To determine

To show that two triangles are congruent.

Answer to Problem 28PSC

  $\Delta ABC and\Delta FDEarecongruent.$

Explanation of Solution

Given information:

  $TheverticesareA=\left(0,7\right),B=\left(-4,0\right),C=\left(0,0\right),D=\left(2,3\right),E=\left(2.-1\right)andF=\left(9,-1\right).$

Formula used:

The below properties are used:

If the angles are right angles they are congruent.

Two triangles are congruent by SAS congruence rule.

Proof:

From figure,we get

  $BC=4,DE=4,so\overline{BC}\cong \overline{DE}.$

  

  $\angle BCAand\angle DEFarerightangles,sotheyarecongruent.$

  $CA=7,EF=7,so\overline{CA} \cong \overline{EF}.$

By SAS congruence rule,

  $\Delta ABC \cong \Delta FDE$