Triangle ABC is dilated by a scale factor of 7 4 to generate triangle WXY.

Which of the following expressions could be used to determine the length of WX ?

A.
Correct!

B.
Incorrect. WX corresponds with AB, not AC.

C. WX = 2 1 4 ÷ 7 4
Incorrect. When a triangle is dilated by a scale factor, the side length of the original triangle is multiplied by the scale factor.

D. WX = 1 1 2 ÷ 7 4
Incorrect. When a triangle is dilated by a scale factor, the side length of the original triangle is multiplied by the scale factor. Also, WX corresponds with AB, not AC.

Hexagon ABCDEF is a dilation of hexagon QRSTUV.

Which of the following is a true statement?

A.  AB RS = DE TU
Incorrect. A dilation generates two similar figures, and corresponding sides of two similar figures have proportional lengths. AB and RS are not corresponding sides.

B. AB BC = BC CD
Incorrect. A dilation generates two similar figures, and corresponding sides of two similar figures have proportional lengths. AB and BC are not corresponding sides, and neither are BC and CD.

C.  AB QR = DE TU
Correct!

D.  AF QV = TU DE
Incorrect. AF and QV are corresponding sides, and so are TU and DE, so their lengths are proportional. However, when writing the proportion, once the first ratio is written, the second ratio must have numerators and denominators that correspond to the parts in the first ratio.

Parallelogram WXYZ is a dilation of parallelogram ABCD.

Which of the following is a true statement?

A. AB corresponds with XY.
Incorrect. ∠A and ∠X are not corresponding angles, so these two sides cannot be corresponding.

B. CD corresponds with YZ.
Correct!

C. CD corresponds with WZ.
Incorrect. ∠C and ∠W are not corresponding angles, so these two sides cannot be corresponding.

D. Not here
Incorrect. A dilation generates two similar figures, and similar figures have pairs of corresponding sides.

In the figure below, points A, D, F, and H lie on line a. Triangles AFE and AHG are dilations of triangle ADC.

Based on the information in the figure, which of the following statements is true?

A. CD EF = AC AE
Correct!

B. GH EF = AH AD
Incorrect. GH and EF are corresponding sides from similar triangles AHG and AFE. However, AH and AD are not from the same two similar triangles, so their ratio is not going to be equal to the first ratio.

C. AC AG = CD EF
Incorrect. AC and AG are corresponding sides from similar triangles ADC and AHG. However, CD and EF are not from the same two similar triangles, so their ratio is not going to be equal to the first ratio.

D. GH EF = AH AE
Incorrect. AH and AE are not corresponding sides.

Triangle JKL is a dilation of triangle ABC.

Which of the following is a true statement?

A. AB corresponds with LJ.
Incorrect. ∠A and ∠L are not corresponding angles, so these two sides cannot be corresponding.

B. AB JK = AC LK
Incorrect. AB and JK are corresponding sides, but AC and LK are not. Since these are not both pairs of corresponding sides, this proportion may not be true.

C. BC KL = AC JK
Incorrect. BC and KL are corresponding sides, but AC and JK are not. Since these are not both pairs of corresponding sides, this proportion is not true.

D. Not here
Correct! None of the three provided statements are true.