Chapter 6.1, Problem 59SPR

To determine

The comparison between the given measures.

Answer to Problem 59SPR

  $JM>ML$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Hinge Theorem, if the two sides of a triangle are congruent to the two sides of another triangle, and also if the included angle measure of the first triangle is larger than the included angle measure of the second triangle, then the third side of the first triangle is larger than the third side of the second triangle.

Consider the given triangles;

According to the Reflexive Property of Congruence:

  $\begin{array}{l}\overline{KM}\cong \overline{KM}\\ \overline{KJ}\cong \overline{KL}\left(given\right),\\ m\angle JKM>m\angle LKM\left(given\right),\end{array}$

According to the Hinge theorem;

  $JM>ML$