Chapter 5, Problem 16PT

To determine

To Find: The comparison for the given measures.

Answer to Problem 16PT

The converse of the hinge theorem shows that $m\angle RSR>m\angle JKL$ .

Explanation of Solution

Given:

The given measures are $\angle RST$ and $\angle JKL$ .

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the two sides of the triangle are congruent to two sides of another triangle and the third side in the first is longer than the third side of the other triangle. In this case the included angle measure of the first one is more than the included angle measure of the second triangle.

Consider the triangle given then $RS=KJ$ so one has $\overline{RS}\cong \overline{KJ}$ .

Since $ST=KL$ one has $\overline{ST}\cong \overline{KL}$ .

Then $RT>LJ$ .

Thus, the converse of the hinge theorem shows that $m\angle RSR>m\angle JKL$ .