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