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

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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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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