Chapter 12.6, Problem 17E

To determine

To Show: The triangle is congruent according to the pattern ASA.

Answer to Problem 17E

The required has been proved.

Explanation of Solution

Given information:

The figure is given by,

  

The properties are given $M$ is the midpoint of $\overline{NL}$ , $\overline{NL}\perp \overline{NQ}$ , $\overline{NL}\perp \overline{MP}$ , and $\overline{QM}\parallel \overline{PL}$

As it is given that $M$ is the midpoint of $\overline{NL}$ and a midpoint cuts a segment into two congruent halves.

  $\overline{NM}\cong \overline{ML}$

It is given that $\overline{NL}\perp \overline{NQ}$ and $\overline{NL}\perp \overline{MP}$ , and a perpendicular become a right angle to corresponding line.

  $\angle QNM\cong \angle PML$ because both are right angles.

As it given that $\overline{QM}\parallel \overline{PL}$ , $\angle QMN\cong \angle PLM$ .

So, the triangle follows the ASA pattern. That means $\Delta NQM\cong \Delta MPL$ .

Therefore, the required has been proved.