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Consider the Base Angles Theorem.
If XZ ≅ XY, then ∠XZY ≅ ∠ZYX
Base Angles Theorem
The given statement, XZ≅ XY, tells us that these sides are congruent. Let's add this to the diagram.
According to the Base Angles Theorem, if two sides of a triangle are congruent, then the angles opposite them are congruent.
We can use this to complete the if-then statement. If XZ ≅ XY, then ∠XZY ≅ ∠ZYX.