Q. 85.0( 3 Votes )

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


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.


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