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Presentation Lesson Review of Pythagorean Theorem Important vocabulary words are highlighted in red. • Theorem: A statement that has been proven to be true based on existing truths. Used mostly in mathematics. • Example: • In MN, trees bloom in March and April. Based on geographic location of MN and the position of the earth to the sun. Pythagorean Theorem Given a right triangle with sides a and b and hypotenuse c, a2 + b2 = c2. b a c This theorem is attributed to Pythagoras, a Greek mathematician and philospher who lived circa 580’s BCE. • Right triangle – a triangle in which one angle is 90o. • The hypotenuse is the side of a triangle with the longest length. hypotenuse 90o • Now do Worksheet B to derive Pythagorean Theorem for yourself. • Another way to view the Pythagorean Theorem. • Find the area of the inside small square, Asmall. The length of a side of the big square is 2 and its area is, Abig=4. • Find x. x s=2 (Mazur, 2003, p.9) • A visual of the Pythagorean Theorem. (Wikipedia, 2012). • Use the Pythagorean Theorem to solve for the unknown side. x 7 5 x 7 (7)2 + (5)2 = x2 49 + 25 = x2 74 = x2 x = √74 5 x 12 (12)2 + (5)2 = x2 144 + 25 = x2 169 = x2 x = 13 5 A Pythagorean triplet has three integers for the lengths of the sides of a triangle. Some examples of triples: (3,4,6) ( 5, 12, 15) (7,24,25) (8,15,17) • Now consider the case where the triangle is either a isosceles triangle or an equilateral triangle. An isosceles triangle is a triangle with two sides of equal length. An it’s acute angles are 45o. • An acute angle is angle that is less than 90o. acute angles • The sides of an equilateral triangle all have equal length. Each angle has 60o. • Discussion of isosceles triangle. • Discussion of equilateral triangle. • Discussion finding the lengths of sides of similar triangles. A similar triangle has the same angles, but may have different lengths of sides. A ratio is the a number that compares the length of one side to another side of a triangle. • Sample word problems. References: Wikipedia (2012). Retrieved on 2/24/12 from http://en.wikipedia.org/wiki/Pythagoras. Mazur, B. (2003). Imaginary Numbers (particularly the square root of minus fifteen). New York: Farrar, Straus and Giroux