Question

complete the proof that ( \triangle efgcong\triangle ehg ).

Explanation:

Step1: Identify the given congruent segments

From the figure, we can see that the marks on the segments indicate congruence. So, for $\overline{GH}\cong\overline{FG}$, the reason is "Given (marked on the figure)".

Step2: For $\overline{EF}\cong\overline{EH}$

Similarly, the reason is "Given (marked on the figure)".

Step3: For $\overline{EG}\cong\overline{EG}$

This is the reflexive property of congruence (a segment is congruent to itself).

Step4: Prove $\triangle EFG\cong\triangle EHG$

Since we have three pairs of congruent sides ($\overline{EF}\cong\overline{EH}$, $\overline{FG}\cong\overline{GH}$, $\overline{EG}\cong\overline{EG}$), by the SSS (Side - Side - Side) congruence criterion, $\triangle EFG\cong\triangle EHG$.

Answer:

1. Given (marked on the figure)
2. Given (marked on the figure)
3. Reflexive property of congruence
4. SSS (Side - Side - Side) congruence criterion