Chapter 5.6, Problem 11PPS

To determine

To find:Thelarger angle between $\angle MLP$ and $\angle TSR$ .

Answer to Problem 11PPS

The angle $m\angle MLP<m\angle TSR$ .

Explanation of Solution

Given Information:

The given figure is

  

Formula Used:

Hinge theorem is

If two sides of a triangle correspond to two sides of another triangle, and the angle of inclination of the first triangle is greater than the angle of inclination of the second triangle, so the sides of the first triangle are longer than the sides of the third side of the second triangle.

From the figure, $\overline{LM}\cong \overline{ST}$ and $\overline{LP}\cong \overline{SR}$ , and $MP<TR$ , then the measure of the angles opposite $\overline{MP}$ and $\overline{TR}$ are related as $m\angle MLP<m\angle TSR$ used the converse of the Hinge Theorem.

Hence, the angle $m\angle MLP<m\angle TSR$ .