Subject :IMO Class : Class 9

In Δ*DEF* and Δ*PQR*, *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.