Chapter 4.1, Problem 11WE

(a)

To determine

To find: Thetriangle that is congruent to $\Delta PAL$ .

Answer to Problem 11WE

  $\Delta RLA$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

Asthe two triangles are congruent,thus $\Delta PAL$ is congruent to $\Delta RLA$ .

Therefore, $\Delta PAL\cong \Delta RLA$ .

To determine

(b)

Answer to Problem 11WE

  $\overline{PA}\cong \overline{RA}$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As $\Delta PAL\cong \Delta RLA$ , the corresponding parts of the congruent triangles are also congruent.

Therefore, $\overline{PA}\cong \overline{RA}$ .

To determine

(c)

Answer to Problem 11WE

  $\angle 3$ and $\overline{RL}$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As, $\Delta PAL\cong \Delta RLA$ , the corresponding parts of the congruent triangles are also congruent.

Therefore, $\angle 1\cong \angle 3$ .

As, alternate interior angles $\angle 1\cong \angle 3$ are equal, therefore $\overline{PA}$ is parallel to $\overline{RL}$ .

To determine

(d)

Answer to Problem 11WE

  $\angle 4$ and $\overline{PL}$ is parallel to $\overline{AR}$ .

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As, $\Delta PAL\cong \Delta RLA$ , the corresponding parts of the congruent triangles are also congruent.

Therefore, $\angle 2\cong \angle 4$ .

Since, alternate interior angles $\angle 2\cong \angle 4$ are equal, thus $\overline{PL}$ will be parallel to $\overline{AR}$ .

So, $\angle 2\cong \angle 4$ and $\overline{PL}$ is parallel to $\overline{AR}$ .