Question

1. state if the triangles in each pair are similar. if so, state how you know they are similar. a) not similar b) yes, aa similarity c) yes, sss similarity d) yes, sas similarity

Explanation:

Step1: Calculate side - length ratios

Calculate the ratios of corresponding sides. $\frac{PQ}{MN}=\frac{56}{20}=\frac{14}{5}$, $\frac{PR}{LN}=\frac{84}{30}=\frac{14}{5}$, $\frac{QR}{LM}=\frac{112}{40}=\frac{14}{5}$.

Step2: Apply similarity criterion

Since $\frac{PQ}{MN}=\frac{PR}{LN}=\frac{QR}{LM}$, by the SSS (Side - Side - Side) similarity criterion, the two triangles are similar.

Answer:

c) Yes, SSS Similarity