Chapter 3, Problem 46CUR

To determine

To prove: that $\overline{RS}\parallel \overline{UT}$ .

Explanation of Solution

Given information:

The given information is follows

  $\overline{RU}\parallel \overline{ST},\angle R\cong \angle T$

Proof:

From the given data

  $\overline{RU}\parallel \overline{ST}$ and $\overline{US}$ is transversal.

  $\angle 1\cong \angle 2$

  $\angle R\cong \angle T$ and $\overline{US}$ is common to $\Delta URS\text{ and }\Delta UTS$ .

  $\Rightarrow \Delta URS\cong \Delta UTS$

For similar triangles the corresponding angles are congruent.

  $\Rightarrow \angle 3\cong \angle 4$

  $\Rightarrow \overline{RS}\parallel \overline{UT}$

Hence, proved.