Schoolcrop

Solution :

Given : ∆ABC ∼ ∆XYZ

R.T.P :

∆ABC

∆XYZ

AD²

XW²

Proof :We know that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

∆

∆XYZ

AB²

.....(1) [∵ ∆ABC ∼ ∆XYZ]

In ∆ABD and ∆XYW

∠B = ∠

∠D = ∠ = °

From AA similarity,

∆ ∼ ∆

∴

∆ABD

∆XYW

.....(2)

From (1) and (2),

∆

Hence the ratio of areas of two similar triangles is to the squares of ratio of their corresponding medians.

(Q6) Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding medians.