Hello from MrBillDoesMath!
Answer: The solution is presented below. Hope it helps
Discussion:
1) Triangle XYB is similar to triangle AYZ.
(They have two angles in common, a right angle and angle X or Z (given).
Since the sum of the angles of a triangle is 180, and the triangles have
two identical angles, the remaining angles in the triangle are also the
same. Hence the triangles similar by the AAA theorem)
2) As triangle YXB is similar to triangle YZA, corresponding parts are in the
same ratio, so
AZ/BX = XY/ZY
But we are given than XY = ZY so
AZ/BX = XY/ZY = 1
which implies that AZ is congruent to BX.
Thank you,
MrB
