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14.2 October 23, 2013 14.2 Pythagorean Theorem The Pythagorean Theorem What does it say? What does it really mean? How do we use it? Find the missing side: 10cm 6cm 10 cm 7cm 1 14.2 October 23, 2013 What is the longest segment you can get on a geoboard? What is the second longest? Third? 2 14.2 October 23, 2013 A Geometric Representation: 3 14.2 October 23, 2013 Pythagorean Triples You will need a sheet of graph paper. On your graph paper, draw a vertical segment the number of units in length that is designated in the table. Draw a horizontal segment using the table below and then measure or compute the hypotenuse. Vertical 5 6 8 12 15 Horizontal Hypotenuse 12 8 15 16 20 4 14.2 October 23, 2013 Carpet proof http://www.youtube.com/watch? v=pVo6szYE13Y&feature=related 5 14.2 October 23, 2013 An Indian Proof b2 a2 6 14.2 October 23, 2013 Garfield's Proof R M L U a = short leg b = long leg K c = hypotenuse MLKR is a _______________________________ ∆ MUR is ___________ _______________ triangle; why? area of MLKR = Area of the three triangles = ________+___________+_____________ 7 14.2 October 23, 2013 Can we use Pythagorean Theorem to find the diagonal length of a unit cube? 8 14.2 October 23, 2013 9 14.2 October 23, 2013 10 14.2 October 23, 2013 11 14.2 October 23, 2013 12 14.2 October 23, 2013 13 14.2 October 23, 2013 14 14.2 October 23, 2013 15 14.2 October 23, 2013 16