Question

consider the two triangles shown. which statement is true? the given sides and angles cannot be used to show similarity by either the sss or sas similarity theorems. the given sides and angles can be used to show similarity by the sss similarity theorem only. the given sides and angles can be used to show similarity by the sas similarity theorem only. the given sides and angles can be used to show similarity by both the sss and sas similarity theorems.

Explanation:

Step1: Check SAS similarity

For SAS similarity, we need to check if the ratio of two sides is equal and the included angle is equal.
Let's assume \(\triangle HFG\) and \(\triangle JLK\).
\(\frac{HF}{JL}=\frac{48}{12} = 4\), \(\frac{FG}{LK}=\frac{32}{8}=4\)
The included angles (the non - marked angles which are equal as the triangles have the given angle - side - angle relation in terms of similarity check)
So, by SAS similarity (if the ratio of two sides is equal and the included angle is equal), we can check similarity.

Step2: Check SSS similarity

For SSS similarity, we need to check \(\frac{HF}{JL}=\frac{FG}{LK}=\frac{HG}{JK}\)
\(\frac{HF}{JL}=\frac{48}{12} = 4\), \(\frac{FG}{LK}=\frac{32}{8}=4\), \(\frac{HG}{JK}=\frac{36}{9}=4\)

Answer:

The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.