Questions: With the information given below, can you conclude that triangle LMN is congruent to triangle XYZ? Yes No

With the information given below, can you conclude that triangle LMN is congruent to triangle XYZ? Yes No
Transcript text: With the information given below, can you conclude that $\triangle L M N \cong \triangle X Y Z$ ? Yes No
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Solution

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Solution Steps

Step 1: Analyze the given information

We are given two triangles, △LMN\triangle LMN and △XYZ\triangle XYZ. We know that LM‾≅XY‾\overline{LM} \cong \overline{XY}, MN‾≅YZ‾\overline{MN} \cong \overline{YZ}, and ∠N≅∠Z\angle N \cong \angle Z. These are two sides and an angle that are congruent between the two triangles.

Step 2: Determine if the information is sufficient to prove congruency

The given information matches the Side-Angle-Side (SAS) postulate if the angle is between the two sides. In △LMN\triangle LMN, the angle NN is between sides LMLM and MNMN. Similarly, the angle ZZ is between sides XYXY and YZYZ in △XYZ\triangle XYZ. Therefore, the SAS postulate applies.

Final Answer:

Yes

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