# Prove that

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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