Questions: What additional information is needed to prove the 2 triangles are congruent by the listed theorem? ∠ GIH = ∠ MKL MK = GI ∠ MLK = ∠ GHI

What additional information is needed to prove the 2 triangles are congruent by the listed theorem? ∠ GIH = ∠ MKL MK = GI ∠ MLK = ∠ GHI
Transcript text: What additional information is needed to prove the 2 triangles are congruent by the listed theorem? $\angle \mathrm{GIH}=\angle \mathrm{MKL}$ $\overline{M K}=\mathrm{GI}$ $\angle \mathrm{MLK}=\angle \mathrm{GHI}$
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Solution

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Solution Steps

Step 1: Analyze the given information

We are given two triangles, $\triangle$MKL and $\triangle$GIH. We are also told that LK $\cong$ IH. We are looking for the additional information needed to prove the triangles congruent by SAS.

Step 2: Determine what SAS means

SAS stands for Side-Angle-Side. This means we need two congruent sides and the included angle between those sides to be congruent.

Step 3: Determine the solution

We are given that LK $\cong$ IH. To have SAS, we need the angles between these sides to be congruent and the other sides next to the angles to be congruent. So, we need ∠LKM $\cong$ ∠GHI and MK $\cong$ GI.

Final Answer: The correct answer is MK = GI.

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