Please answer the foll:question

Asked by ashwati | 8th Mar, 2009, 06:07: PM

Expert Answer:

Let the point of intersection of DF and AE be G.(say)

D and F are given as midpoints of AB and AC.

So DF is parallel to BC and half of it (mid point thm)

Now consider triangle ABE.

 

D is the mid point of AB and DG parallel to BE.

So,

So G must be the mid point of AE( converse of mid point thm)

i.e.

So we can say that DF bisects AE.

Next,

E is the mid point of BCand G is the mid point of  AE.

So,DG=1/2(BE)=1/4(BC)

Simly,

GF=1/4(BC)

So,

 DG=GF

So,

 AE bisects DF

Thus we have proved that

AE  and DF bisect each other.

Answered by  | 8th Mar, 2009, 07:56: PM

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