Question

refer to the figure shown to the right. if ∠feg = ∠heg and ∠fge = ∠hge, then prove that △efg ≅ △ehg. complete the proof below. statements reasons 1. 1. given 2. 2. given 3. 3. 4. △efg ≅ △ehg 4. therefore, △efg and △ehg are congruent by the asa property of congruence.

Explanation:

Step1: State first given angle

$\angle FEG=\angle HEG$

Step2: State second given angle

$\angle FGE=\angle HGE$

Step3: Identify common side

$EG = EG$ (Reflexive property of equality)

Step4: Apply congruence criterion

Since two - angles and the included side of $\triangle EFG$ are equal to two - angles and the included side of $\triangle EHG$, by the ASA (Angle - Side - Angle) congruence criterion, $\triangle EFG\cong\triangle EHG$.

Answer:

1. $\angle FEG=\angle HEG$
2. $\angle FGE=\angle HGE$
3. $EG = EG$, Reflexive property of equality
4. ASA property of congruence