Lesson 8.1.notebook
February 04, 2013
Lesson 8.1 ‐ The Pythagorean Theorem and Its Converse
Theorem 8.1 ‐ Pythagorean Theorem
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
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A Pythagorean triple is a set of nonzero whole numbers a, b, and c that sasfy the equaon a 2 + b2 = c2
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Lesson 8.1.notebook
Ex 1:
February 04, 2013
Pythagorean Triples
a)
A right triangle has legs of length 16 and 30. Find the length of the hypotenuse. Do the lengths of the sides form a Pythagorean triple?
b)
A right triangle has a hypotenuse of length 25 and a leg of length 10. Find the length of the other leg. Do the lengths of the sides form a Pythagorean Triple?
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Lesson 8.1.notebook
February 04, 2013
Ex 2: A baseball diamond is a square with 90‐ sides. Home plate and second base are at opposite verces of the square. About how far is home plate from second base?
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Lesson 8.1.notebook
February 04, 2013
Theorem 8.2 ‐ Converse of the Pythagorean Theorem
If the square of the length of one side of a triangle is equal to the sum of the squares of the length of the other two sides, then the triangle is a right triangle.
Ex 3: A triangle has side lengths 7, 4, and 6. Is the triangle a right triangle?
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Lesson 8.1.notebook
February 04, 2013
Theorem 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, the triangle is obtuse.
If c2 > a2 + b2, the triangle is obtuse
Theorem 8.4
If the 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, the triangle is acute.
If c2 < a2 + b2, the triangle is acute
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Lesson 8.1.notebook
Ex 4:
February 04, 2013
The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right.
a) 15, 20, 25
b) 10, 15, 20
c) 7, 8, 9
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Lesson 8.1.notebook
February 04, 2013
Homework: Page 420 #2‐26 EVEN, 27‐29, 36‐39, 48
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