Question

AXYZ is a dilation of AABC by a scale factor of 5. Which of the following proportions verifies that AABC and AXYZ are similar?

A. (frac{AB}{BO} = frac{AC}{XZ})
B. (frac{AB}{AC} = frac{XZ}{OD})
C. (frac{AC}{XZ} = frac{OD}{AB})
D. (frac{AC}{XZ} = frac{XZ}{AC})

Answer 1

The correct proportion that verifies that triangles AABC and AXYZ are similar is b)(frac{AB}{AC} = frac{XZ}{OD}).

Step-by-step explanation:

The correct proportion that verifies that triangles AABC and AXYZ are similar is:

(frac{AB}{AC} = frac{XZ}{OD})

This proportion compares the lengths of corresponding sides in the two similar triangles. In a dilation, corresponding sides are in proportion to the scale factor. So, the length of side AB in triangle AABC is in proportion to the length of side XZ in triangle AXYZ and the length of side AC in triangle AABC is in proportion to the length of side OD in triangle AXYZ. Therefore, the correct proportion is option b) (frac{AB}{AC} = frac{XZ}{OD}).