Answer :

Let triangle be ABC. D, E and F are the midpoints of sides AB, BC and CA, respectively.



By midpoint theorem, for D and E as midpoints of sides AB and BC,


DE ∣∣ AC


Similarly, DF ∣∣ BC and EF ∣∣ AB.


ADEF, BDFE and DFCE are all parallelograms.


But, DE is the diagonal of the BDFE.


BDE FED (1)


Similarly, DF is the diagonal of the parallelogram ADEF.


∆DAF ∆FED …(2)
And, EF is the
diagonal of the parallelogram DFCE.


∆EFC ∆FED …(3)


Hence, all the four triangles are congruent.


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