Question

In the given triangle ABC, AE is the median, FD || BC and ED || AB. Prove that CF is
the median drawn from C to AB.​

Answer 1

In the given triangle ABC, AE is the median.

Also, ED || AB. Therefore, by BPT(Basic Proportionality Theorem) :

• CE/EB = CD/DA

Since CE=EB (E is mid point of BC), CD=DA. Hence D is the mid-point of AC.

Now, as FD || BC, and since D is the mid-point of AC, from BPT:

• AD/DC = AF/FB

Since AD=DC (D is the mid-point of AC), AF=FB. Hence, F is the mid-point of AB

Therefore, CF is the median drawn from C to AB