Chapter 3.3, Problem 4PSA

To determine

To show that two sides are congruent.

Answer to Problem 4PSA

  $\overline{XT}and\overline{XR}arecongruent.$

Explanation of Solution

Given information:

  $\begin{array}{l}TandRtrisect\overline{SW}.\hfill \\ \overline{XS} \cong \overline{XW}\hfill \\ \angle S \cong \angle W\hfill \end{array}$

Formula used:

The below properties are used:

If a segment is trisected, it is divided into three congruent segments.

Two triangles are congruent by SAS congruence rule.

Proof:

It is given that,

  $TandRtrisect\overline{SW}.$

  

If a segment is trisected, it is divided into three congruent segments.

  $\overline{ST} \cong \overline{RW}\cong \overline{TR}$

It is given that,

  $\overline{XS} \cong \overline{XW}$

  $\angle S \cong \angle W$

By SAS congruence rule, we get

  $\Delta XST \cong \Delta XWR$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{XT} \cong \overline{XR}$