MAT 115 PROJECT I PYTHAGOREAM THEOREM PAING SOE 05/11/2006 Topics covered Introduction of the Pythagorean Theorem Explanation of the Pythagorean Theorem Proof of the Pythagorean Theorem Usefulness of the Pythagorean Theorem Introduction of Pythagorean Theorem Definition of Pythagorean Theorem History of Pythagorean Theorem Definition of Pythagorean Theorem The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. History of the Pythagorean Theorem One of the earliest theorems known to ancient civilizations. It was named after the Greek mathematician and philosopher, “Pythagoras”. History of P.T Pythagoras was also the founder of the Pythagorean school of mathematics in Southern Italy. However, we do not know for sure that “Pythagoras” himself proved the P.T as he refused to record his findings. Explanation of Pythagorean Theorem Figure presentation of P.T Proof of the P.T As the sum of the area of the two rectangles and the squares: (a+b)2 = a2 + 2ab + b2 As the sum of the areas of a square and the four triangles: (a+b)2 = c2 + 4(ab/2) = c2 + 2ab Now, setting the two right hand side expressions in these equations equal, gives: a2 + b2 +2ab = c2 + 2ab a2 + b2 = c2 Usefulness of Pythagorean Useful since in the middle school It becomes more important during the high school years With the help of technology and other educational resources, students should be able to see the better usefulness of P.T Other Usefulness Pythagorean has helped Hockey Society to calculate the winning percentage. GF^2 ------------GF^2 + GA^2 where GF = goal scored , GA = goal allowed QUESTIONS ?