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.

To prove the similarity theorem, ratio of corresponding side and corresponding angle should be equal. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems. Hence, the correct option is D.

Given:

Consider the two triangles shown.

Triangles FGH and LKJ are shown.

Angles HFG and KLJ are congruent. The length of side FG is 32, and the length of side JL is 8.

The length of side HG is 48 and the length of side KJ is 12. The length of side HF is 36 and the length of side KL is 9.

As per mentioned in question, Angles HFG and KLJ are congruent.

[tex]\frac{FG}{JL}=\frac{32}{8}=4:1\\\frac{HG}{KJ}=\frac{48}{12}=4:1\\\frac{HF}{KL}=\frac{36}{9}=4:1 \\\angle F=\angle L\\\angle H=\angle K\\\angle G=\angle J[/tex]

Here, ratio of corresponding sides are equal and corresponding angles of triangles are also equal.

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

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