Given that ∠F = ∠Z and DF = XZ, which of the following conditions must be true for △DEF and △XYZ to be congruent?
EF = YZ by SAS criteria
In △DEF and △XYZ, the given equal angle ∠F = ∠Z is included between the sides DF and EF in △DEF and between the sides XZ and YZ in △XYZ.
DF = XZ is already given. For the SAS congruence rule, the other pair of sides forming the equal angle must also be equal, i.e. EF = YZ.
With EF = YZ, the two sides adjacent to the equal included angle are equal, so △DEF ≅ △XYZ by the SAS criteria.
Hence, the answer is EF = YZ by SAS criteria.
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