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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