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.