Tag: proof

Proofs of angle in a semicircle theorem

The Angle in a Semicircle Theorem states that the angle subtended by a diameter of a circle at the circumference is a right angle. An alternative statement of the theorem is the angle inscribed in a semicircle is a right angle. Proof Draw a radius of the circle from C. This makes two isosceles triangles….

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Multiples of 3 and Consecutive Numbers

Numbers that are multiples of 3 are 3, 6, 9, 12, …. Problem Prove that numbers that are multiples of 3 can be expressed as sum of three consecutive numbers. Solution (2 out of 5 marks) 3 = 0 + 1 + 2 6 = 1 + 2 +3 9 = 2 + 3 +…

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