Caroline is given this diagram and told that ¯¯EG¯ is an angle bisector of ∠HEF. She looks carefully and finds one pair of congruent angles between two pairs of congruent sides. She determines that the triangles must be congruent by the SAS Congruent Theorem. Match each pair of congruent corresponding parts with the reason Caroline knows that they are congruent (3 points)

Question

¯¯EG¯ ≅ EG¯
∠HEG ≅ ∠FEG
HE¯¯¯ ≅ FE¯¯¯
and
given in the diagram
reflexive property of congruence
angle bisectors create congruent angles

Answer 1

To match each pair of congruent corresponding parts with the reasons Caroline knows they are congruent, we could structure the information as follows:

1. ¯¯EG¯ ≅ EG¯

   • Reason: Reflexive property of congruence

2. ∠HEG ≅ ∠FEG

   • Reason: Angle bisectors create congruent angles

3. HE¯¯¯ ≅ FE¯¯¯

   • Reason: Given in the diagram

This layout pairs each congruent part with its respective reason, showing how Caroline deduced the congruences of the triangles.