Ex 6.2, 7 - Prove that line drawn through mid-point of one - Ex 6.2

 

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Ex 6.2, 7 Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX). Given: Let us assume Δ ABC Where DE is parallel to BC & D is the mid point of AB To prove: E is the mid point of AC Proof: In Δ ABC , DE II BC 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 𝐴𝐷/𝐷𝐵=𝐴𝐸/𝐸𝐶 𝐷𝐵/𝐷𝐵=𝐴𝐸/𝐸𝐶 1 =𝐴𝐸/𝐸𝐶 EC = AE ⇒ E is the mid-point of AC Hence proved

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