Answer
The triangles are similar by the Side-Side-Side (SSS) Similarity Theorem.
Work Step by Step
We are given the measures of all the sides in the two triangles. Let's see if the Side-Side-Side Similarity Theorem can be applied here.
The SSS Similarity Theorem states that if three sides in one triangle are proportional to the three sides of another triangle, then the two triangles are similar.
Let's set up the ratios of corresponding sides in the two triangles:
First set of corresponding sides = $\frac{9.6}{6.4}$
First set of corresponding sides = $\frac{3}{2}$
Let's look at the second pair of corresponding sides:
Second set of corresponding sides = $\frac{21}{14}$
Second set of corresponding sides = $\frac{3}{2}$
Let's look at the third pair of corresponding sides:
Third set of corresponding sides = $\frac{27}{18}$
Third set of corresponding sides = $\frac{3}{2}$
All corresponding sides in both triangles have the same scale factor or ratio, meaning the sides are proportional, so the triangles are similar by the Side-Side-Side (SSS) Similarity Theorem.
