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Question

D,E,F are the mid points of the sides AB,BC,CA respectively of ABC. Then DEF is congruent to

A
ABC
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B
AEF
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C
BDF,CDE
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D
ADF
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Solution

The correct option is D ADF
Given: ABC, D,E and F are mid points of AB,BC,CA respectively.
In ABC
F is mid point of AC and D is mid point of AB.
Thus, By Mid point theorem
FD=12CB and FD=CB or FD=CE and FDCE ....(1)
Similarly,
DE=FC and DEFC ...(2)
FE=DB and FEDB ...3)
From (1), (2) and (3)
ADEF, DBEF, DECF are parallelograms
The diagonal of a parallelogram divides the parallelogram into two congruent triangles.
Hence, DEFADF
DEFDBE
DEFFEC
DEFADFECFADF

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