ASK Rare Notes – Study Notes & Exam Preparation

Pythagorean Theorem, its proofs and applications: Introduction: Pythagoras was a Greek mathematician and philosopher. He was born in 570 BC, on the island of Samos. One of the famous relics of Pythagoras is the Pythagoras’ Theorem; after his name, which states "In a right triangle it is true that the square of the hypotenuse is equal to the sum of the squares of the other two sides". The hypotenuse is the longest side of a right triangle. There are various methods of proving this theorem. We shall prove it by using similar triangles. Statement: In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Figure: Given: 1. ∆ACB is a right-angled triangle. Figure (i) 2. Where m∠C = 90° and m = a, m = b and m = c. To Prove: c² = a² + b² Construction: 1. Draw a perpendicular from C on. 2. m = h, m = x and m = y. 3. c = x + y 4. The ∆ABC is now split int...