Question

Which proportion best completes the proof showing that ΔWXZ ~ ΔXYZ, given that segment XZ is perpendicular to segment WY and angles WZX and XZY are both right angles and congruent?

A. 16/12 = 9/12
B. 16/12 = 12/9
C. 12/12 = 16/9
D. 12/16 = 16/9

Answer 1

The correct proportion that completes the proof showing that ΔWXZ ~ ΔXYZ is option D (12/16 = 16/9). Hence the correct answer is option D

Step-by-step explanation:

The correct proportion that completes the proof showing that ΔWXZ ~ ΔXYZ is option D (12/16 = 16/9).

To understand why, we can use the concept of similarity of triangles. Given that segment XZ is perpendicular to segment WY and angles WZX and XZY are both right angles and congruent, we can conclude that ΔWXZ and ΔXYZ are similar triangles.

Similar triangles have proportional sides. In this case, we can set up a proportion between the side lengths of the two triangles. In ΔWXZ, the side WX corresponds to the side XY in ΔXYZ. Similarly, the side WZ corresponds to the side XZ. Therefore, we can write the proportion as 12/16 = 16/9, or option D.