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Question
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
Options
ABC
AEF
BFD, CDE
AFE, BFD, CDE
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Solution
It is given that D, E and Fare the mid points of the sides BC , CA and AB respectively of ΔABC
FE =BD (By mid point theorem)
BD = DC (As it is mid point)
Now in ΔAFE and ΔDFE
FE(Common)
DF = AE (Mid point)
AF = DE (Mid point)
⇒ ΔFED ≅ ΔBFD
⇒ ΔDFE ≅ ΔDCE
Hence (d)
ΔDFE ≅ AFE
≅ BFD
≅ CDE
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