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# 1 CT PPT How Zhao Yin Ho Qi Yan Ong Ru Yun Pythagoras and the Pythagorean Theorem 2014

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### 1 CT PPT How Zhao Yin Ho Qi Yan Ong Ru Yun Pythagoras and the Pythagorean Theorem 2014

1. 1. NAME : HOW ZHAO YIN (201420026) HO QI YAN (201420009) ONG RU YUN (201420030) CLASS : FOUNDATION IN LIBERAL ARTS MODULE : INTRODUCTION TO CRITICAL THINKING LECTURER : MS. DOT MACKENZIE TERM : MAY 2014 DATE : 14 JULY 2014 TOPIC : PYTHAGORAS AND THE PYTHAGOREAN THEOREM
2. 2. PYTHAGORAS AND THE PYTHAGOREAN THEOREM Illustration source: http://www.edb.utexas.edu/visionawards/petrosino/Media/Members/zhfbdzci/pythagoras1.gif According to the UALR (2001), “The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.-500 B.C.), who was perhaps the first to offer a proof of the theorem. But people had noticed the special relationship between the sides of a right triangle long before Pythagoras.”
3. 3. WHERE WAS PYTHAGORAS BORN? Samo s Illustration source: http://intmstat.com/blog/2008/03/samos.jpg
4. 4. WHAT IS PYTHAGOREAN THEOREM? According to the UALR (2001), “The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse, or, in mathematical terms, for the triangle shown at right, a2 + b2 = c2. Integers that satisfy the conditions a2 + b2 = c2 are called "Pythagorean triples." ”
5. 5. RIGHT-ANGLED TRIANGLE Illustration source: http://www.mathopenref.com/images/triangle/hypotenuse.gif
6. 6. Illustration source: http://www.mathsaccelerator.com/measurement/images/triangle-answer.gif Right-Angled Triangle
7. 7. HOW TO PROVE THE EQUATION OF PYTHAGOREAN THEOREM? c b a •There are four similar triangle with the rotation of different angle which are 90°, 180°, and 270°. •Area of triangle can be calculated by using this formulae: ½ x a x b
8. 8. •The four triangles combined together to form a square shape with a square hole. •The length of side of square inside is a-b. •The area of square inside is (a-b)² or 2ab. •The area of four triangles is 4(½ x a x b). In the last, we get this formulae c²= (a - b)² + 2ab = a² - 2ab + b² + 2ab = a² + b²
9. 9. Illustration source: http://cdn.instructables.com/FN4/7VG4/GVZPOZOZ/FN47VG4GVZPOZOZ.MEDIUM.gif