8-4 Similarity in Right Triangles

8-4 Similarity in Right Triangles - geometric mean of the...

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Similarity in Right Similarity in Right Triangles Triangles Section 8-4
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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. 8-3 Thm. 8-3 The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
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A B D C ~ ADC CDB ACB :
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Corollary 1 to Thm 8-3 Corollary 1 to Thm 8-3 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
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a h b b h h a =
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Corollary 2 to Thm. 8-3 Corollary 2 to Thm. 8-3 The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the
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Unformatted text preview: geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. 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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8-4 Similarity in Right Triangles - geometric mean of the...

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