Question

How are the triangles similar? Triangle 1 sides 96,80,64 Triangle 2 sides 54,36,45

A. SSS
B. SAS
C. AA
D. Not similar

Answer 1

Triangles with corresponding side lengths having the same ratio are similar by the Side-Side-Side (SSS) similarity criterion. The side lengths of Triangle 1 (96, 80, 64) and Triangle 2 (54, 45, 36) give the same ratio when compared, confirming that they are similar by SSS, answer option A.

Step-by-step explanation:

To determine whether the triangles are similar through side lengths, we can examine the corresponding side ratios. For similar triangles, all corresponding side ratios should be equal, following Side-Side-Side (SSS) similarity criterion.

For Triangle 1 with sides 96, 80, 64, and Triangle 2 with sides 54, 45, 36, we find the ratios of corresponding sides:

• 96/54
• 80/45
• 64/36

When calculated, we get:

• 1.777(Repeating)
• 1.777(Repeating)
• 1.777(Repeating)

Since the ratios of all corresponding sides are equal, we can conclude that the two triangles are similar by the SSS (Side-Side-Side) criterion. Hence, the correct answer is A. SSS.