Chapter 5.6, Problem 1CYU

To determine

To find: The larger angle between $m\angle ABC$ and $m\angle GDE$ .

Answer to Problem 1CYU

The angle $m\angle ABC>m\angle GDE$ .

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, $\overline{AC}\cong \overline{GD}$ . Segment $AC$ measures $5$ and segment $GD$ measures $5$ , so they have equal measures and rare therefore congruent.

Now, $\overline{BC}\cong \overline{ED}$ , Segment $BC$ measures $4$ and segment $ED$ measures $4$ , so they have equal measures and rare therefore congruent

Again, $AB>GE$ Segment $AB$ measures $3.2$ and segment $GE$ measures $3$ .

  $m\angle ACB>m\angle GDE$

Thus by converse of the Hinge theorem, $\angle ACB$ is greater than $\angle GDE$ .

Hence, $m\angle ABC>m\angle GDE$ .