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geomtery 8.1 The Pythagorean Theorem

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by

Mr. Simpson

on 6 December 2013

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Transcript of geomtery 8.1 The Pythagorean Theorem

Finally
Pythagorean Theorem
8.1 The Pythagorean Theorem and its converse
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.
Pythagorean Triple
Pythagorean Triple is a set of nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem equation.
If you were on the beach on the southeast corner of a lake and wanted to go across to reach the northwest corner of a lake how far would you have to travel by boat if the northwest beach was 176 meters west and 330 meters north of the southeast beach.
Find the length of the missing side
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 lengths of the other two sides, then the triangle is a right triangle.
What do you notice if you square the length of the sides of each triangle?
(leg)
(leg)
(Hypotenuse)
1.) 3, 4, 5
2.) 5, 12, 13
3.) 8, 15, 17
4.) 7, 24, 25
5.) 9, 40, 41
Common Pythagorean Triple's
1.)
8
15
17
Is this a Pythagorean triple?
If you multiply each number in a Pythagorean Triple by the same whole number, the 3 numbers that result also form a Pythagorean triple.
12
16
20
3(4), 4(4), 5(4)
24
10
X
41
9
X
Solve for X.
Find the value of x. Make sure to leave your answer in simplest radical form and not decimal.
20
8
______
______
______
If
the triangle is
acute
If
the triangle is
obtuse
Is it a right triangle if the sides of a triangle are 8, 10, 12?
Classify the triangle whose side lengths are 15, 7, 11.
Pythagorean Theorem
where
C
is the
hypotenuse
where
C
is the
hypotenuse
X
1.
2.
Full transcript