In a Δ 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.

Question

In a &#x394; 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.

Philoid · Accepted Answer

Given,

In ΔABC,

E & F are the mid-points of AC and AB

EF ⎸⎸BC

SO, FQ ⎸⎸BP

Q is the mid point of AP

AQ = QP (Proved)