Chapter 4.4, Problem 8CE

To determine

Whether the given statement is true or false.

Answer to Problem 8CE

The given statement is a true statement.

Explanation of Solution

Given information :

It is given $\overline{MK}\cong \overline{NK}\iff \angle 3\cong \angle 4$

Consider the triangle $\Delta KMN$ shown in figure.

Given that $\overline{MK}\cong \overline{NK}$

From isosceles triangle theorem if two sides of a triangle are congruent, then the angles opposite those sides are congruent.

So $\angle 3\cong \angle 4$

Conversely,

Given that $\angle 3\cong \angle 4$

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Therefore, $\overline{MK}\cong \overline{NK}$

Therefore, the given statement is a true statement.