In the triangle ABC ,D is the midpoint of the side BC . From the point D parallel
straight lines CA and BA intersect the sides BA and CA at the point of E and F
respectively. Let us prove that EF=1/2 BC.
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Step-by-step explanation:
Since,D is the midpoint of bc and
DF parallel to AB
so, F is also the mid point of AC by converse of mid point theorem.
then AF=FC......(i)
also, D is the mid point of BC and
ED parallel to AC
so, E is also mid point of AB by coverse of mid point theorem
then AE = EB .....(ii)
from equation i and ii we have:
AF/FC=AE/EB
so now by converse of midpoint theorem
EF is parallel to BC and EF=1/2 BC.
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