Question

aisha is trying to determine if △lmn and △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 side lengths

For $\triangle LMN$: $LN = 6$, $MN = 7$, $LM = 11$.
For $\triangle PQR$: $PR = 12$, $QR = 14$, $QP = 22$.

Step2: Check ratios of corresponding sides

Calculate ratios:
$\frac{LN}{PR} = \frac{6}{12} = \frac{1}{2}$,
$\frac{MN}{QR} = \frac{7}{14} = \frac{1}{2}$,
$\frac{LM}{QP} = \frac{11}{22} = \frac{1}{2}$.

Step3: Apply SSS similarity

Since all three corresponding sides are in proportion ($\frac{1}{2}$), by SSS (Side - Side - Side) similarity theorem, the triangles are similar.

Answer:

The triangles are similar by the SSS similarity theorem.