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ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD ⊥ AC Q.7(1-2)

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Yesterday i was doing the question from class 9th ncert book of math of Quadrilaterals chapter of exercise 8.2   What is the easiest way for solving it because i was not able to do this question please help me for solving this question ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD ⊥ AC

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  1. Ncert solutions class 9 chapter 8-18

    (i) In ΔACB,

    M is the midpoint of AB and MD || BC

    , D is the midpoint of AC (Converse of mid point theorem)

    (ii) ∠ACB = ∠ADM (Corresponding angles)

    also, ∠ACB = 90°

    , ∠ADM = 90° and MD ⊥ AC

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