ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB an parallel to BC intersects AC at D. Show that
MD $⊥$ AC [4 MARKS]

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Solution

Diagram : 1 Mark
Concept : 1 Mark
Proof : 2 Marks

Given , ABC is a right angled triangle.

$∠ C = 90^{\circ}$

And M is the mid-point of AB.

Also, $M D ∥ B C$

Since, $M D ∥ B C$ and $C D$ is transversal.

$∴ ∠ A D M = ∠ A C B$ ( Corresponding angles)

But $∠ A C B = 90^{\circ}$

$∴ A D M = 90^{\circ}$

$\Rightarrow M D ⊥ A C$

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ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB an parallel to BC intersects AC at D. Show that MD ⊥ AC [4 MARKS]

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ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB an parallel to BC intersects AC at D. Show that
MD $⊥$ AC [4 MARKS]