Question

In a triangle ABC ,E and F are the mid points of AC and AB respectively. The altitude AP to BC intersects EF at Q. Prove that AQ=QP

Answer 1

Hey,

In triangle ABC,

F is the mid point of AB

E is the mid point of AC

Therefore,

FE//AB & FE=1/2AB(Mid point theorem).

Now,

In triangle ABP,

F is the mid point of AB

FQ//BP(FQ and BP are parts of FE and BC respectively)

Therefore,

Q is the mid point of AP(Converse of mid point theorem)

Hence, AQ=QP.

Hence, proved.

Hope this helps you!!!!