Question

question 17 of 45
△uvw is a dilation of △rst by a scale factor of 1. which of the following proportions verifies that △rst and △uvw are similar?
a. $\frac{rs}{uv}=\frac{uw}{sr}$
b. $\frac{rs}{st}=\frac{wv}{vu}$
c. $\frac{rt}{st}=\frac{uw}{uv}$
d. $\frac{rs}{uv}=\frac{rt}{uw}$

Explanation:

Step1: Recall similarity - proportion rule

For similar triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

In \(\triangle RST\) and \(\triangle UVW\), \(RS\) corresponds to \(UV\), \(ST\) corresponds to \(VW\), and \(RT\) corresponds to \(UW\).

Step3: Check each option

• Option A: \(\frac{RS}{UV}=\frac{UW}{SR}\) is incorrect as the right - hand side ratio is not a correct corresponding - side ratio.
• Option B: \(\frac{RS}{ST}=\frac{VW}{VU}\) is incorrect as the sides are not paired correctly for similar - triangle proportions.
• Option C: \(\frac{RT}{ST}=\frac{UW}{VW}\) is incorrect as the sides are not paired correctly for similar - triangle proportions.
• Option D: \(\frac{RS}{UV}=\frac{RT}{UW}\) has the correct corresponding - side ratios.

Answer:

D. \(\frac{RS}{UV}=\frac{RT}{UW}\)