Q18 of 32 Page 6

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.(CBSE 2002, 04, 05, 06, 08, 09, 10)


Let us assume ΔABC & ΔPQR are similar


Area of ΔABC = 0.5 ×AD ×BC


Area of ΔPQR = 0.5 ×PS ×QR


Now since the two triangles are similar so the length of sides and perpendiculars will also be in proportion


…Equation 1


…Equation 2


From Equation 1 We get



Putting in Equation 2 we get



⇒


So we can see ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides


Hence Proved

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