ΔDEF and ΔXYZ are two triangles such that ΔXYZ ≅ ΔFDE. If XY = 23 cm, ∠Y = 68° and ∠X = 43°, then which of the following options is correct?
DF = 23 cm, ∠E = 69°
The congruence ΔXYZ ≅ ΔFDE gives the vertex correspondence X ↔ F, Y ↔ D, Z ↔ E, so the matching sides and angles are equal.
Therefore XY = FD, which means DF = 23 cm.
Also ∠Y = ∠D = 68° and ∠X = ∠F = 43°, so ∠E = 180° − 68° − 43° = 69°.
Hence, the answer is DF = 23 cm, ∠E = 69°.
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