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Ex 6.4, 6 - Prove that ratio of areas of two similar triangles - Area of similar triangles

Ex 6.4, 6 - Chapter 6 Class 10 Triangles - Part 2
Ex 6.4, 6 - Chapter 6 Class 10 Triangles - Part 3

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Ex 6.4, 6 Exercise 6.4 Chapter 6 Class 10 CBSE NCERT Maths Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. Given: Let ABC ~ PQR Here AD is median Hence BD = CD = 1/2 BC Similarly, PS is median Hence QS = RS = 1/2 QR To prove: ( )/( )=( / )^2 Proof: Given ABC ~ PQR = Also, / = / / =2 /2 / = / In & = / = / ~ Hence / = / Now, since ABC PQR We know that if two triangles are similar, the ratio of their area is always equal to the square of the ratio of their corresponding side ( )/( ) = ( / )^2 ( )/( ) = ( / )^2 Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.