In triangle WXZ,
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
If ΔYWZ ~ ΔYXW
∠WXY = ∠WZY
Then, we can also conclude
∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.
