We are given two right triangles that have two pairs of proportional corresponding sides. Also, by the definition of right triangles, ∠Y and ∠B are right angles.
Notice that the sides that are proportional are the legs of the triangles, and since all right angles are congruent, we have that ∠Y ≅ ∠B.
∠Y ≅ ∠B and XY/AB = YZ/BC
Therefore, by the Side-Angle-Side (SAS) Similarity Theorem â–³ YXZ ~ â–³ BAC, which is what we wanted to prove.
Two-Column Proof
Given: & â–³ XYZ and â–³ ABC are right
& triangles; XYAB= YZBC
Prove: & â–³ YXZ ~ â–³ BAC
Let's summarize the proof we did above in the following two-column table.
