Example 1 - If a line intersects sides AB and AC of ABC - Theorem 6.1

Example 1 - Chapter 6 Class 10 Triangles - Part 2


Example 1 If a line intersects sides AB and AC of a Ξ” ABC at D and E respectively and is parallel to BC, prove that 𝐴𝐷/𝐴𝐡=𝐴𝐸/𝐴𝐢 Given: Ξ” ABC , where line intersects sides AB and AC at D and E. And DE II BC To Prove : 𝐴𝐷/𝐴𝐡=𝐴𝐸/𝐴𝐢 Proof: We know that if a line drawn parallel to one side of triangle, intersects the other two sides in distinct points, then it divides the other 2 side in same ratio Therefore , 𝐴𝐷/𝐷𝐡=𝐴𝐸/𝐸𝐢 𝐴𝐷/𝐷𝐡=𝐴𝐸/𝐸𝐢 𝐷𝐡/𝐴𝐷 =𝐸𝐢/𝐴𝐸 Adding 1 on both sides 𝐷𝐡/𝐴𝐷+1=𝐸𝐢/𝐴𝐸+1 (𝐷𝐡 + 𝐴𝐷)/𝐴𝐷 =(𝐸𝐢 + 𝐴𝐸)/𝐴𝐸 𝐴𝐡/𝐴𝐷=𝐴𝐢/𝐴𝐸 𝐴𝐷/𝐴𝐡=𝐴𝐸/𝐴𝐢 Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.