In the adjoining figure, are the midpoints of the sides and respectively, of Show that and

Question

In the adjoining figure,  are the midpoints of the sides  and  respectively, of  Show that  and

Philoid · Accepted Answer

Here, in , are the midpoints of the sides and respectively.

By mid point theorem, as F and E are the mid points of sides AB and AC,

FE ∣∣ BC

Similarly, DE ∣∣ FB and FD ∣∣ AC.

Therefore, AFDE, BDEF and DCEF are all parallelograms.

We know that opposite angles in parallelogram are equal.

∴ In AFDE, we have,

∠A = ∠EDF

In BDEF, we have,

∠B = ∠DEF

In DCEF, we have,

∠ C = ∠ DFE

Hence proved.