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Ex 6.4, 4 - If areas of two similar triangles are equal - Area of similar triangles

Ex 6.4, 4 - Chapter 6 Class 10 Triangles - Part 2
Ex 6.4, 4 - Chapter 6 Class 10 Triangles - Part 3

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Ex 6.4, 4 If the areas of two similar triangles are equal, prove that they are congruent. Given: Let triangles be Δ ABC & Δ DEF Both triangles are similar, i.e.,∆ ABC ~∆ DEF and Areas are equal, i.e., ar Δ ABC = ar Δ DEF To prove: Both triangles are congruent, i.e.∆ ABC ≅∆ DEF Proof: Given ∆ ABC ~∆ DEF We know that if two triangle are similar , Ratio of areas is equal to square of ratio of its corresponding sides (𝑎𝑟 ∆ 𝐴𝐵𝐶)/(𝑎𝑟 ∆ 𝐷𝐸𝐹)=(𝐵𝐶/𝐸𝐹 )^2=( 𝐴𝐵/𝐷𝐸 )^2=( 𝐴𝐶/𝐷𝐹 )^2 (𝑎𝑟 ∆ 𝐷𝐸𝐹)/(𝑎𝑟 ∆ 𝐷𝐸𝐹)=(𝐵𝐶/𝐸𝐹 )^2=( 𝐴𝐵/𝐷𝐸 )^2=( 𝐴𝐶/𝐷𝐹 )^2 1 =(𝐵𝐶/𝐸𝐹 )^2=( 𝐴𝐵/𝐷𝐸 )^2=( 𝐴𝐶/𝐷𝐹 )^2 Taking In ∆ ABC a𝑛𝑑 ∆ DEF EF = BC AB = DE AC = DF Hence by SSS congruency ∆ ABC ≅∆ DEF 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.