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) `M D_|_A C` (iii) `C M = M A=1/2A B`

Explanation

(i)D is the mid-point of AC

`In /_\ABC`

Given : M is the mid-point of AB

& MD || BC

`therefore D` is the mid-point of AC(Converse of mid-point theorem)

(ii) `M D_|_A C`

`DM || CB`, AC is the transversal

`/_MDC + /_DCB = 180^0 `(Co-interior angles)

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