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Using the side lengths shown in the two triangles of Fig. 6.30, which statement is correct?  
A$\triangle ABC \sim \triangle PQR$ by AA similarity
B$\triangle ABC \sim \triangle RQP$ by SSS similarity
C$\triangle ABC \cong \triangle RQP$ by SSS congruence
DThe triangles are not similar because their sizes are different
Answer & Solution
Correct answer: B. $\triangle ABC \sim \triangle RQP$ by SSS similarity
From Fig. 6.30, $\frac{AB}{RQ}=\frac{3.8}{7.6}=\frac12$, $\frac{BC}{QP}=\frac{6}{12}=\frac12$, and $\frac{CA}{PR}=\frac{3\sqrt3}{6\sqrt3}=\frac12$. Since all corresponding sides are proportional, the triangles are similar by SSS. They are not congruent because their corresponding sides are not equal.
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