Question

complete the proof that $\triangle efh \cong \triangle eig$.

(image of a triangle with points f, g, h, i, e, and some angle and segment markings)

statement	reason
2 $\angle f \cong \angle i$	given
3 $\angle feg \cong \angle hei$	given
4 $m\angle gei = m\angle geh + m\angle hei$
5 $m\angle feh = m\angle feg + m\angle geh$	additive property of angle measure
6 $m\angle gei = m\angle geh + m\angle feg$
7 $m\angle feh = m\angle gei$	transitive property of equality
8 $\triangle efh \cong \triangle eig$	aas

Explanation:

Step1: Identify reason for Step4

This uses the additive property of angle measure, as $\angle GEI$ is split into $\angle GEH$ and $\angle HEI$.

Step2: Identify reason for Step6

Substitute $\angle HEI$ with $\angle FEG$ (given congruent, so equal measure) in Step4's equation. This is the Substitution Property of Equality.

Answer:

1. Reason for Statement 4: Additive Property of Angle Measure
2. Reason for Statement 6: Substitution Property of Equality