7-1 and 7-2 Geometric Mean and Pygthagorean Thm

7-1 and 7-2 - measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg d h e a b c d a a c = e b b c = Pythagorean Theorem

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Geometric Mean & Geometric Mean & the Pythagorean Thm. the Pythagorean Thm. Section 7-1 & 7-2
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The geometric mean between 2 positive numbers a and b is the positive number x where x 2 = ab x = b x x a = ab
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Thm. 7-1 Thm. 7-1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the 2 triangles formed are similar to the given triangle and to each other.
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A B D C CDB ADC ~
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Thm. 7-2 Thm. 7-2 The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the 2 segments of the hypotenuse.
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a h b b h h a =
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Thm. 7-3 Thm. 7-3 If the altitude is drawn to the hypotenuse of a right triangle, then the measure of a leg of the triangle is the geometric mean between the
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Unformatted text preview: measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg. d h e a b c d a a c = e b b c = Pythagorean Theorem Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. a b c a 2 + b 2 = c 2 Converse is also true. Pythagorean Triples Pythagorean Triples If the measures of a right triangle are whole numbers, the measures of the sides are a Pythagorean triple. 3-4-5 5-12-13 8-15-17 7-24-25 Joke Time Joke Time What is a twip? A twip is what a wabbit takes when he wides on a twain. What is gray, has big ears and has a trunk? A mouse going on vacation...
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This note was uploaded on 12/01/2011 for the course MATH 105 taught by Professor Towns during the Fall '10 term at BYU.

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7-1 and 7-2 - measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg d h e a b c d a a c = e b b c = Pythagorean Theorem

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