Question

write a congruence statement and give a reason why the triangles are congruent. select the correct choice below and, if necessary, write the letters of the second triangle in the correct order. a. $\triangle nlm \cong \triangle \square$ by sss b. $\triangle nlm \cong \triangle \square$ by sas c. the two triangles are not necessarily congruent. there is not enough information. help me solve this view an example get more help - clear all

Explanation:

Step1: Analyze Triangle Congruence

To determine triangle congruence, we use criteria like SSS (Side - Side - Side), SAS (Side - Angle - Side), etc. For SSS, all three corresponding sides of two triangles must be equal. For SAS, two sides and the included angle must be equal.

Step2: Evaluate the Options

• Option A: If we assume the triangles have all three corresponding sides equal (SSS), then \(\triangle NLM\cong\triangle\) (the other triangle) by SSS. We need to check if the side - length information (even if not fully visible, the option is structured for SSS) holds.
• Option B: SAS requires two sides and the included angle. The option's structure for SAS may not match the given triangle configuration (since the problem's context, even with partial visibility, leans more towards SSS if the sides are marked equal).
• Option C: Saying there's not enough info or they are not congruent is incorrect if the SSS criteria is met.

Answer:

A. \(\triangle NLM\cong\triangle\) (the other triangle) by SSS