Chapter 4.5, Problem 15WE

To determine

To prove: that $\angle 4\cong \angle 5$ with the help of given information.

Answer to Problem 15WE

  $\angle 4\cong \angle 5$ is proved.

Explanation of Solution

Given information:

Given: $\angle 1\cong \angle 2\cong \angle 3$ ; $\overline{EN}\cong \overline{DG}$

Calculation:

Showing that $△MEN\cong △MDG$

Consider these two triangles and follow the following steps provided

Statement	Reason
$\angle 1\cong \angle 2\cong \angle 3$	Provided
$\overline{ME}\cong \overline{MD}$	If two angles of a triangle are congruent, Then the side opposite those angles is congruent
$\overline{EN}\cong \overline{DG}$	Proved
$△MEN\cong △MDG$	By SAS postulate
$\angle 4\cong \angle 5$	CPCT

Therefore, the triangles $\text{Δ}MEN$ and $\text{Δ}MDG$ are congruent by Side Angle Side (SAS) property

This implies that by Congruent Parts of Congruent Triangles (CPCT) are equal, that is $\angle 4\cong \angle 5$