Chapter 7.5, Problem 45SPR

To determine

To Prove: $\Delta EFG\cong \Delta HFG$ if $\overline{EF}\cong \overline{HF}$ and $G$ is the midpoint of $E\overline{H}$ .

Explanation of Solution

Given:A flock of geese flies in the formation.

  

  $S-A-S$ congruence states that if two sides and angle between them of two triangles are congruent, then the triangles are said to be congruent by $S-A-S$ congruence rule.

Suppose, in triangles $\Delta EFG,\Delta HFG$ , $\overline{EF}\cong \overline{HF}$ and $G$ is the midpoint of $E\overline{H}$

In other words, $\overline{GE}\cong \overline{GH}$ and $\overline{EF}\cong \overline{HF}$ .

Also, the angle between the two sides:

  $\angle FGH\cong \angle FGE=90°$

Therefore, by $S-A-S$ congruence:

  $\Delta EFG\cong \Delta HFG$