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 CM=MA=12AB [4 MARKS]
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Solution
Diagram : 1 Mark Concept : 1 Mark Proof : 2 Marks
Consider a right angle ΔABC right angled at C.
⇒∠C=90∘
And M is the mid-point of AB. and DM ∥ BC
⇒D is the midpoint of AC [By converse of midpoint theorem]