Chapter 5.3, Problem 6PSA

To determine

To Find: Whether the lines $\overline{TX}\parallel \overline{EW}$ ?

Answer to Problem 6PSA

  $\overline{TX}\parallel \overline{EW}$

Explanation of Solution

Given:

  

  $\overline{TE}\parallel \overline{XW}\text{and }\overline{TE}\cong \overline{XW}$

Concept Used:

Alternate interior angles are equal when two parallel lines are intersected by a transversal.

Calculation:

Joins T, W, E, X T, X, E, and W we get

  

  $\begin{array}{l}\text{In }\Delta TEW\text{ and }\Delta TXE\\ \Rightarrow \overline{TE}\cong \overline{XW}\\ \Rightarrow \angle ETW=\angle XWT\\ \Rightarrow WT=WT\left(\text{Common side}\right)\\ \Rightarrow \Delta TEW\cong \Delta TXE\\ \Rightarrow \angle TEW=\angle TXW\\ \Rightarrow \overline{TX}\parallel \overline{EW}\\ \text{and }\overline{TX}\cong \overline{EW}\\ \therefore \overline{TX}\parallel \overline{EW}\end{array}$