Question

In the adjoining figure, D, E, F are the midpoints of the sides BC, CA and AB respectively, of △ ABC. Show that ∠ EDF = ∠ A, ∠ DEF = ∠ B and ∠ DFE = ∠ C.

Answer 1

Consider △ AFE and △ DFE

Using the midpoint theorem

AF = ½ AB = ED

AE = ½ AC = FD

FE is common i.e. FE = EF

By SSS congruence criterion

△ AFE ≅ △ DFE

∠ A = ∠ FDE (c. p. c. t)

In the same way we get ∠ B = ∠ DEF and ∠ C= ∠ DFE.

Therefore, it is proved that ∠ EDF = ∠ A, ∠ DEF = ∠ B and ∠ DFE = ∠ C.