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Question

D, E, F are the midpoints of the sides BC, CA and AB respectively of  ABC. Then  DEF is congruent to triangle – 


  1. ABC

  2. AEF

  3. BFD, CDE

  4. AFE, BFD, CDE


Solution

The correct options are
B

AEF


C

BFD, CDE


D

AFE, BFD, CDE


 It is easy to verify that DEF is congruent to each one of the triangles AEF, BFD & CDE.

Consider ΔAFEAFE=BandAEF=C 

Since FE is parallel to BC.

Similarly in ΔBFDBFD=AandBDF=C  and

 ΔDECDEC=AandEDC=B 

We know A+B+C=180

Now, consider ΔDEFFED=180DBFEDC=180CB=A
Similarly, DFE=C and FED=B.
By AA similarity
So, ΔDEF~ΔAFE~ΔBFD~ΔCDE

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