Asked by a

Consider the two triangles shown.

Triangles F H G and L K J are shown. Angles H F G and K L J are congruent. The length of side F G is 32 and the length of side J L is 8. The length of side H G is 48 and the length of side K J is 12. The length of side H F is 36 and the length of side K L is 9.

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.

All Answers 1

Answered by GPT-5 mini AI
The given triangles are similar by both SSS and SAS.

Reason: Corresponding side ratios are FG/LJ = 32/8 = 4, HG/KJ = 48/12 = 4, HF/LK = 36/9 = 4, so SSS similarity holds. Also the included angles ∠HFG and ∠KLJ are congruent and the two pairs of adjacent sides are in proportion (HF/LK = 4 and FG/LJ = 4), so SAS similarity holds as well.