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Using theorem 6.2 , prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX). Q.8

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What is the best way to solve the problem of exercise 6.2 of triangles chapter of math, how i solve this problem because it is very important Using theorem 6.2 , prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

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  1. Given, in ΔABC, D and E are the mid points of AB and AC respectively, such that,

    AD=BD and AE=EC.

    Ncert solutions class 10 chapter 6-11

    We have to prove that: DE || BC.

    Since, D is the midpoint of AB

    ∴ AD=DB

    ⇒AD/BD = 1……………………………….. (i)

     

    Also given, E is the mid-point of AC.

    ∴ AE=EC

    ⇒ AE/EC = 1

    From equation (i) and (ii), we get,

    AD/BD = AE/EC

    By converse of Basic Proportionality Theorem,

    DE || BC

    Hence, proved.

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