Download Geometry 8.1 The Pythagorean Theorem and Its Converse A. The

Geometry
8.1 The Pythagorean Theorem and Its Converse
A.
The Pythagorean Theorem and Its Converse
Pythagorean Theorem (Thm 8.1): In a right triangle, the sum of the squares of •
the lengths of the legs is equal to the square of the length of the hypotenuse. a2 + b2 = c2
NOTE: The Pythagorean theorem can only be used in right triangles
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A Pythagorean triple is a set of nonzero whole numbers, a, b and c that satisfy the equation a2 + b2 = c2 . Simply put, they are the lengths of the sides of a right triangle, where the largest number is the length of the hypotenuse
EXAMPLES: 3, 4, 5 and 5, 12, 13, and 8, 15, 17, and 7, 24, 25 are some common •
examples. In addition, if you multiply each number in any of the above Pythagorean triples by the same number, that new set of three is also a Pythagorean triple. For example, multiply 3, 4, 5 by the number 2 and your new triple is 6, 8 10.
Converse of the Pythagorean Theorem ( Thm 8.2): If the square of the length of •
one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle
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B. Use the Pythagorean Theorem to find the missing side. In number 6, tell whether or not the triangle is right.
1.
2.
3.
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4.
5.
6.
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C. Acute and Obtuse Triangles
Thm 8.3 : If the square of the length of the longest side of a triangle is •
greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse. If a2 + b2 < c2, the triangle is obtuse
Thm 8.4 : If ths square of the length of the longest side of a triangle is •
less than the sum of the squares of the lengths of the other two sides, then the triangle is acute. If a2 + b2 > c2, , the triangle is acute
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D. Classify the following triangles with side lengths given as acute, obtuse or right. 1. 15, 20, 25
2, 7, 3, 6
3. 6, 7, 8
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E.
Applications: 1. A baseball diamond is a square with 90 foot sides. Home plate and second base are at opposite vertices of the square. About how far is home plat from second base? Round to nearest whole number.
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8.1 HW p. 420 #s 1 ­ 16, 18 ­ 23, 27, 28
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