Question

select the true statement in reference to the triangles.

(first triangle with sides 37.5, 57, 87.5)

(second triangle with sides 15, 25, 38)

Explanation:

To determine the true statement about the triangles, we check for similarity by verifying if the ratios of corresponding sides are equal.

Step 1: Calculate the ratio of the first pair of sides

The first sides of the triangles are \( 37.5 \) (top triangle) and \( 15 \) (bottom triangle). The ratio is:
\[
\frac{37.5}{15} = 2.5
\]

Step 2: Calculate the ratio of the second pair of sides

The second sides are \( 57 \) (top triangle) and \( 25 \) (bottom triangle). The ratio is:
\[
\frac{57}{25} = 2.28
\]

Step 3: Calculate the ratio of the third pair of sides

The third sides are \( 87.5 \) (top triangle) and \( 38 \) (bottom triangle). The ratio is:
\[
\frac{87.5}{38} \approx 2.3026
\]

Since the ratios of the corresponding sides are not equal (\( 2.5
eq 2.28
eq 2.3026 \)), the triangles are not similar.

(Note: If there were options provided, we would compare these ratios to the given statements. Since the problem asks to select the true statement and we assume the context is about similarity, the true statement would be that the triangles are not similar because the ratios of corresponding sides are not equal.)

If we assume the possible options were about similarity (e.g., "The triangles are similar" or "The triangles are not similar"), the true statement is that the triangles are not similar.

Answer:

The triangles are not similar (because the ratios of corresponding sides \( \frac{37.5}{15}=2.5 \), \( \frac{57}{25}=2.28 \), \( \frac{87.5}{38}\approx2.30 \) are not equal).