Question

determine whether the given triangles are similar. if they are, write a similarity statement and name the postulate or theorem you used. if the triangles are not similar, explain why. choose the correct answer below. a. △abc∼△hkg by the sas - theorem. b. △abc∼△hkg by the aa - postulate. c. △abc∼△hkg by the sss - theorem. d. △abc and △hkg are not similar because the corresponding sides of the triangles are not in proportion.

Explanation:

Step1: Check side - length ratios

Calculate the ratios of corresponding sides. $\frac{AB}{HK}=\frac{52}{13} = 4$, $\frac{AC}{HG}=\frac{24}{6}=4$, $\frac{BC}{KG}=\frac{44}{11} = 4$.

Step2: Apply similarity theorem

Since $\frac{AB}{HK}=\frac{AC}{HG}=\frac{BC}{KG}$, by the SSS - Similarity Theorem, the triangles are similar. The similarity statement is $\triangle ABC\sim\triangle HKG$.

Answer:

C. $\triangle ABC\sim\triangle HKG$ by the SSS - Theorem.