Question

Consider the two triangles shown.

A. The given sides and angles cannot be used to show similarity by either the SSS or SAS similarity theorems.
B. The given sides and angles can be used to show similarity by the SSS similarity theorem only.
C. The given sides and angles can be used to show similarity by the SAS similarity theorem only.
D. The given sides and angles can be used to show similarity by both the SSS and SAS similarity theorems.

Answer 1

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

Explanation:

Edge 2020 (2021)

Answer 2

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

Explanation:

step 1

we know that

The SSS Similarity Theorem , states that If the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

In this problem

`(HG)/(JK)=(GF)/(JL)=(HF)/(KL)`

Verify

substitute the values

`(48)/(12)=(32)/(8)=(36)/(9)`

`4=4=4` ---> is true

therefore

The triangles are similar by SSS similarity theorem

step 2

we know that

The SAS Similarity Theorem , states that two triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

In this problem

Two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal

therefore

The triangles are similar by SAS similarity theorem