Question

asha is trying to determine if $\triangle lmn$ and $\triangle pqr$ are similar, congruent, or neither using the information in the diagram.
which statement is true?
○ the triangles are not similar, but they are congruent.
○ the triangles are neither similar nor congruent.
○ the triangles are similar by the sas similarity theorem.
○ the triangles are similar by the sss similarity theorem.

Explanation:

Step1: Identify triangle side lengths

$\triangle LMN$ sides: $MN=7$, $NL=6$, $LM=11$
$\triangle PQR$ sides: $QP=22$, $PR=12$, $RQ=14$

Step2: Calculate side ratios

$\frac{MN}{RQ} = \frac{7}{14} = \frac{1}{2}$, $\frac{NL}{PR} = \frac{6}{12} = \frac{1}{2}$, $\frac{LM}{QP} = \frac{11}{22} = \frac{1}{2}$

Step3: Match to similarity theorem

All corresponding side ratios are equal, so SSS similarity applies.

Answer:

The triangles are similar by the SSS similarity theorem.