Chapter 4.5, Problem 18PPS

To determine

To prove:

  $\overline{FH}\cong \overline{JG}$ for the following figure in the form of the paragraph:

  

Explanation of Solution

Given information:

  $\begin{array}{l}\angle F\cong \angle J\\ \overline{FH}\cong \overline{GJ}\end{array}$

Proof:

From the given figure:

  

Know that $\overline{FH}$ is parallel to $\overline{GJ}$ and $\angle F\cong \angle J$ . Here, $\angle FHG$ and $\angle JGH$ are alternate interior angles so $\angle FHG\cong \angle JGH$ . The measure of angle $CED$ is $90°$ i.e. since $\overline{EA}$ perpendicular to $\overline{AB}$ . Use the angle side angle (ASA) congruence postulate gets that $\Delta GHJ\cong \Delta HGF$ . Know that corresponding parts of congruent triangles are congruent so, $\overline{FH}\cong \overline{JG}$ .

Hence proved.