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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
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Solution

## The correct option is D △ADFGiven: △ABC, D,E and F are mid points of AB,BC,CA respectively.In △ABCF is mid point of AC and D is mid point of AB. Thus, By Mid point theoremFD=12CB and FD=CB or FD=CE and FD∥CE ....(1)Similarly,DE=FC and DE∥FC ...(2)FE=DB and FE∥DB ...3) From (1), (2) and (3)□ADEF, □DBEF, □DECF are parallelogramsThe diagonal of a parallelogram divides the parallelogram into two congruent triangles.Hence, △DEF≅△ADF△DEF≅△DBE△DEF≅△FEC△DEF≅△ADF≅△ECF≅△ADF

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