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Subject :IMO    Class : Class 9

In ΔDEF and ΔPQR, DE = DF, ∠F = ∠P and ∠E = ∠Q. The two triangles are

A Isosceles but not necessarily congruent
B Isosceles and congruent
C Congruent but not isosceles
D Neither congruent nor isosceles

The answer should be (B). It is because if angleE = angleQ and angleF = angleP, then angleD = angleR so the triangles are similar. Also, we can see that angleE = angleQ and angleF = angleP, so DE = QR and DF = PR, but DE=DF, so QR=PR and hence both triangles are both congruent and isosceles.

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