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Question

D, E and F are respectively mid points of sides ¯¯¯¯¯¯¯¯AB,¯¯¯¯¯¯¯¯BC and ¯¯¯¯¯¯¯¯CA of ΔABC. Which of the following correspondence between ΔABC and ΔDEF of similarity.
625656_d299e2be78d44d94900551b475f9d892.png

A
ABCEFD
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B
ABCFED
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C
ABCDEF
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D
ABCEDF
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Solution

The correct option is A ABCEFD
D, E and F are the mid-points of the sides AB, BC and CA of Δ ABC.
FD || BC
FD=12BCFDBC=12
DE || AC
DE=12ACDEAC=12
EF || AB
EF=12ABEFAB=12

Then, quadrilaterals ADEF,BEFD,CFDE will be ||gm
A=EandB=FandC=D
ABCEFD
664444_625656_ans_7e34fbe99abe4225bc77695aaa16f700.png

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