Question

ABC is a triangle D is the midpoint of AC. P is a point on AB. through B is a line drawn parallel to PD intersecting AC at Q. show that area of triangle APQ = 1/2 area of triangle ABC

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

Given: In ∆ABC, P is the mid point of BC. PQ||CA, PQ meets AB in Q. QR||BC, QR meets AP in R.

To prove: 1. AP = 2 AR

2. BC = 4 QR

Proof:

In ∆ABC, P is the mid point of BC and PQ||AB.

∴ Q is the mid point of AB (Converse of mid-point theorem)

In ∴ ABP, Q is the mid point of AB and QR||BP.

∴ R is the mid point of AP. (Converse of mid point theorem)

⇒ AP = 2AR

In ∆ABP, Q is the mid point of AB and R is the mid point of AP.