Question

Segment GE is an angle bisector of both angle HEF and angle FG H. Prove triangle HGE is congruent to triangle FGE.

Answer 1

To prove triangle HGE is congruent to triangle FGE, we can use the Angle-Angle-Side (AAS) congruence postulate.

Step-by-step explanation:

Given: Segment GE is an angle bisector of both angle HEF and angle FG H.

To prove triangle HGE is congruent to triangle FGE, we can use the Angle-Angle-Side (AAS) congruence postulate.

1. Since GE is an angle bisector of angle HEF and angle FG H, the angles HGE and FGE are congruent.
2. Angle HGE is congruent to angle FGE (given).
3. Segment GE is congruent to itself (reflexive property).

Therefore, triangle HGE is congruent to triangle FGE by the AAS congruence postulate.