Chapter 6.5, Problem 4ST2

To determine

To complete: the given statement using $<,=\text{ or }>$ .

Explanation of Solution

Given information:

The given figure is as follows:

  

The given statement is “ $\overline{AG}\cong \overline{ER,}\overline{AP}\cong \overline{EN,}$ and $\angle A\cong \angle E$ , then $GP\underset{\_}{}RN$

Concept used:

The side-angle-side postulate:

If two sides and included angle of one triangle is equal to the two sides and angle of the

another triangle, then the two triangles are congruent.

Consider the given statement.

By using the side-angle-side postulate, the two triangles $\Delta AGP\&\Delta ERN$ are

congruent.

So, $GP=RN$

Hence, $GP\underset{\_}{\text{ = }}RN.$