Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.
Given: In a right-angled ΔABC, ∠B=90o. D is the midpoint of hypotenuse AC. DB is joined.
To prove: BD = 12AC
Construction: Draw a circle with centre D and AC as diameter.
∴ The circle drawn on AC as diameter will pass through B.
∴ BD is the radius of the circle.
But AC is the diameter of the circle and D is mid piont of AC.
∴ AD = DC = BD