Q5 of 23 Page 1

Solve any two sub-questions:

Prove that “That ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”


Consider ∆ABC ~ ∆DEF


and height of ∆ABC be h1 and ∆DEF be h2


corresponding sides of similar triangles (i)


∠ABC = ∠DEY … corresponding angles of similar triangles(ii)


Consider ∆ABX and ∆DEY


∠AXB = ∠DYE = 90°


From equation (ii)


∠ABC = ∠DEY


∴by AA test for similarity ∆ABX ~ ∆DEY



But from figure AX = h1 and DY = h2



A(∆ABC) = (1/2)×BC×h1


A(∆DEF) = (1/2)×EF×h2



Using equation (iii) and (i)



Squaring equation (i) and using it in (iv)



Hence proved


Therefore, ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.


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