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

Explanation

DE||BA and DE`=(1)/(2) BA rArr` DE||FA and DE = FA.
`therefore DEAF` is a ||gm.
So, `angle EDF= angle A " " ["opposite " angle " of a ||gm"].`
Similarly, `angle DEF = angle B and angle DFE = angle C.`