Question

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

Since LS XZ L LS 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.

Answer 1

To prove ∆WXZ ≈ ∆XYZ, we use the proportion WX/XY = XZ/XZ, which simplifies to WX/XY = 1, confirming the SAS Similarity Postulate due to the congruence of included angles and the proportionality of corresponding sides.

Step-by-step explanation:

To show that ∆WXZ ≈ ∆XYZ, we look for corresponding sides that are proportional. We have the information that angles WZX and XZY are both right angles and congruent. The proportion that can be used to show the sides are proportional is one that compares the lengths of sides opposite these angles in the two triangles. If we let WX correspond to XY and XZ correspond to XZ (since they are the same in both triangles), then a correct proportion would be WX/XY = XZ/XZ. As XZ/XZ is equal to 1, the triangles are similar by the Side-Angle-Side (SAS) Similarity Postulate, since we have one pair of corresponding sides that are proportional and the included angle is congruent.

Answer 2

The answer is 10/5 = 5/2.5

Step-by-step explanation:

This is because it's the only answer that has an equal proportion of 2

10/5 = 2 5/2.5 = 2