ABCD is a parallelogram x and y are mid points of BC and CD. Prove that ar (Δ AXY) = 3/8 ar (|| gm ABCD).

Question

Philoid · Accepted Answer

Given: ABCD is a ||gm with x as midpoint of BC and y as midpoint of CD.

To Prove:

Proof:

Join BD

In Δ BCD and Δ CXY,

Hence, Δ BCD ≈ Δ CXY

By the property of Similar Triangles,

Area of Δ AXY = Area of || gm – (Area of Δ ABX + Area of Δ CXY + Area of Δ AYD)

Area of Δ AXY = Area of ||gm – (1/8 Area of ||gm ABCD + 1/4 Area of ||gm ABCD + 1/4 Area of ||gm ABCD)

Hence, Proved.