8-1: The Pythagorean Theorem and its Converse Learning Goal: Use the Pythagorean Theorem to calculate the length of the side of a right triangle or determine if a triangle is right. The Pythagorean Theorem ONLY works on RIGHT triangles! EX: A 15 ft ladder is leaning against a building. It reaches a window that is 9 ft off the ground. How far from the building is the base of the ladder? You try! A ramp is built to make a building wheelchair assessable. The ramp begins 24 ft from the building and rises to a vertical height of 7 ft. How long is the ramp? Will the sides always be whole numbers? NO! Pythagorean Triples – 3 whole numbers that satisfy the Pythagorean Theorem (no decimals or fractions) Shortcut for Pythagorean Theorem! Most common ones are 3 – 4 – 5 5 – 12 – 13 7 – 24 – 25 8 – 15 – 17 EX: Do the sides form a Pythagorean Triple? The legs of a right triangle have lengths 10 and 24. what is the length of the hypotenuse? (If you can draw a picture to represent the problem, you don’t have to write the words!) EX: What is the height of the seesaw? Express answer in simplest radical form AND round to the nearest inch. The Converse to the Pythagorean Theorem If a2 + b2 = c2 right triangle If a2 + b2 > c2 acute triangle If a2 + b2 < c2 obtuse triangle EX: Given the 3 side lengths, is each triangle right, acute, or obtuse? A) 85, 84, 13 B) 6, 11, 14 8-1 Assignment: Due Tuesday by the end of class. Workbook pg 203 # 2 – 26 Turn in to the bin by the end of class Tuesday.