Question

Which postulate would you use to justify that triangle XYZ is similar to triangle XAB?

Answer 1

These triangles are similar by the AA Similarity Theorem. The triangles share an angle, which makes the two similar. In addition, the created angles (which come from the parallel lines), forces all of the angles to be congruent, while allowing sides to vary in length.

:)

Answer 2

AA similarity test
Angle YXZ = Angle AXB common angle
Angle YZX = Angle ABX alt angles since the two lines are parallel