Question

In a ΔABC, 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

Proved below.

Step-by-step explanation:

Given:

In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects EF at Q.

To prove:

AQ = QP

Proof:

∴ EF║BC

⇒ FQ║BP

Q is the mid-point of AP.

AQ = QP        [∵F is the mid-point of AB and F║BP]

Hence proved.