Question

Prove when two triangle are similar . The ratio of area of those triangle is equal to rather ratio of the square of there corresponding side

Answer 1

Answer:please see the picture below

Hope it helps you

Please mark me as the brainliest

Step-by-step explanation:

Answer 2

Hence it is proved that when two triangle are similar . The ratio of area of those triangle is equal to rather ratio of the square of there corresponding side.

arΔABC / arΔPQR = (BC/QR)^2 = (AB/PQ)^2 = (AC/PR)^2

Given,

Let the two similar triangles be: Δ ABC and Δ PQR

Let AD and PS be the altitudes of triangles ABC and PQR respectively.

Area of triangle ABC = 1/2 × BC × AD

Area of triangle PQR = 1/2 × QR × PS

ar Δ ABC / ar Δ PQR = 1/2 × BC × AD / 1/2 × QR × PS

ar Δ ABC / ar Δ PQR =  BC × AD / QR × PS

Since the triangles are similar, we have,

AB/PQ = BC/QR = AC/PR = AD/PS .........(1)

ar Δ ABC / ar Δ PQR =  BC × AD / QR × PS

Using (1) we get,

ar Δ ABC / ar Δ PQR =  BC × BC / QR × QR = ( BC / QR )^2

ar Δ ABC / ar Δ PQR = ( BC / QR )^2 = ( AB / PQ )^2 = ( AC / PR )^2

Hence proved.