Question

Which of the following best completes the proof showing that ΔWXZ∼ΔXYZ? Triangles WXZ and XYZ share side XZ with right angle XZW, WZ equals 10, XZ equals 5, and YZ equals 2 and one half. Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion ________ shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate.

(A) WX/XY = XZ/YZ

(B) WX/YZ = XZ/XY

(C) WY/XZ = XW/XY

(D) WY/YZ = WX/XY

Answer 1

The correct proportion to show that ∆WXZ is similar to ∆XYZ is (A) WX/XY = XZ/YZ, as it compares the corresponding legs opposite the congruent right angles, satisfying the SAS Similarity Postulate.

Step-by-step explanation:

The question concerns the proof of similarity between two triangles, ∆WXZ and ∆XYZ, using the SAS Similarity Postulate. To complete the proof, we must show that the corresponding sides of the two triangles are in proportion. Given that triangles ∆WXZ and ∆XYZ are right triangles sharing the right angle at XZ, and that we are provided with the lengths WZ (10), XZ (5), and YZ (2.5), the correct proportion is (A) WX/XY = XZ/YZ. This proportion compares the length of the legs opposite the congruent right angles in each triangle, which is the necessary condition to use the SAS Similarity Postulate. Here WX and XY are the legs opposite the right angles in their respective triangles.