Question

which statement is true for the given triangles?
a the triangles are similar because the ratios of the corresponding sides are the same.
b the triangles are not similar because they are not the same size.
c the triangles are not similar because they are not equilateral.
d similarity cannot be determined because angle measurements are not given.

Explanation:

Step1: Identify sides of each triangle

Triangle VUT: sides are \( VU = 84 \), \( UT = 70 \), \( VT = 42 \)
Triangle QSR: sides are \( SQ = 15 \), \( SR = 30 \), \( QR = 25 \)

Step2: Arrange sides in order and find ratios

Order sides by length:

• Triangle VUT (sorted): \( 42, 70, 84 \)
• Triangle QSR (sorted): \( 15, 25, 30 \)

Now find ratios of corresponding sides:
\( \frac{42}{15} = 2.8 \), \( \frac{70}{25} = 2.8 \), \( \frac{84}{30} = 2.8 \)

All ratios are equal, so by SSS similarity criterion, triangles are similar.

Answer:

A. The triangles are similar because the ratios of the corresponding sides are the same.