Question

ellen dilated △abc to create △qrs. which proportion must be true? choose 1 answer: ① $\frac{ab}{bc}=\frac{qr}{qs}$ ② $\frac{ab}{bc}=\frac{rs}{qr}$ ③ $\frac{bc}{rs}=\frac{qr}{ab}$ ④ $\frac{bc}{rs}=\frac{ab}{qr}$

Explanation:

Step1: Recall dilation property

When a triangle is dilated, the corresponding - side lengths of the original triangle and the dilated triangle are in proportion. That is, if \(\triangle ABC\) is dilated to \(\triangle QRS\), then \(\frac{AB}{QR}=\frac{BC}{RS}=\frac{AC}{QS}\).

Step2: Analyze each option

For option A, the correct proportion should be \(\frac{AB}{QR}=\frac{BC}{RS}\), not \(\frac{AB}{BC}=\frac{QR}{QS}\). For option B, the correct proportion should be \(\frac{AB}{QR}=\frac{BC}{RS}\), not \(\frac{AB}{BC}=\frac{RS}{QR}\). For option C, the correct proportion should be \(\frac{BC}{RS}=\frac{AB}{QR}\), not \(\frac{BC}{RS}=\frac{QR}{AB}\). For option D, since \(\triangle ABC\) is dilated to \(\triangle QRS\), the ratio of corresponding - sides is equal, and \(\frac{BC}{RS}=\frac{AB}{QR}\) is a correct proportion of corresponding - side lengths of the two similar (due to dilation) triangles.

Answer:

D. \(\frac{BC}{RS}=\frac{AB}{QR}\)