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Unformatted text preview: 11-3 The Pythagorean Theorem
A) Theorem 11-8 (The Pythagorean Theorem)
a. b. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. c. Proof: We have a square with a length a+b. In the square we draw four right triangles with legs a and b What do we know about the four triangles? r + s = 90 (why?) r + s + t = 180, so t = Now lets compare the areas of the whole = the parts B) Theorem 11-9
a. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is b. a right triangle, with its right angle opposite the longest side Proof: Given: and let be a right triangle with legs a and b and hypotenuse d. What do we know about d and c? Now the two triangles? Example) Is the following a right triangle.... a) 1,2,3 b) 2,4,7 c) 3,4,5 Example) ...
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