consider the two triangles shown. which statement is true? the given sides and angles cannot be used to show…

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.

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.

Answer

Explanation:

Step1: Check side - side - side (SSS) similarity

For SSS similarity, we need to check if the ratios of corresponding sides are equal. Let's find the ratios of the sides of the two triangles. For (\triangle FGH) and (\triangle JKL), (\frac{FG}{JK}=\frac{32}{8} = 4), (\frac{GH}{KL}=\frac{48}{12}=4), (\frac{FH}{JL}=\frac{36}{9} = 4). Since the ratios of all three pairs of corresponding sides are equal, the SSS similarity theorem can be applied.

Step2: Check side - angle - side (SAS) similarity

For SAS similarity, we need two pairs of corresponding sides in proportion and the included angles equal. We have (\frac{FG}{JK}=\frac{32}{8}=4) and (\frac{FH}{JL}=\frac{36}{9} = 4), and the included angles (\angle HFG) and (\angle LJK) are equal (as they are marked as equal in the figure). So the SAS similarity theorem can also be applied.

Answer:

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