Question

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.​

Answer 1

Answer:

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.