Chapter 6.5, Problem 5ST2

To determine

To Complete: the statement “ $\text{If }\overrightarrow{GA}\cong \overrightarrow{RE},\overrightarrow{GP}\cong \overrightarrow{RN},\text{and}AP>EN,\text{then}m\angle G\underset{\_}{?m\angle R}$ by writing $<,=,\text{or >}$ .

Answer to Problem 5ST2

  $>$

Explanation of Solution

Given:

Figure is shown as:

  

Statement is:

  $\text{If }\overrightarrow{GA}\cong \overrightarrow{RE},\overrightarrow{GP}\cong \overrightarrow{RN},\text{and}AP>EN,\text{then}m\angle G\underset{\_}{?m\angle R}$

Calculation:

Theorem 6-6 states that:

If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.

Since, $\overrightarrow{GA}\cong \overrightarrow{RE},\overrightarrow{GP}\cong \overrightarrow{RN}$ and third side is $AP>EN$ , therefore included angle of the first triangle is larger than the included angle of the second.

That is. $m\angle G>\underset{\_}{m\angle R}$

Therefore, the answer is $>$ .