unit 1.6  exploring the Pythagorean theorem
what we need to know
 Right triangles and the terminology relevant to them.
 Understand the difference between the hypotenuse and the legs of a right triangle.
 Be able to identify the hypotenuse.
 Remember that the area of the square of the hypotenuse is equal to the sum of the areas formed by the other two legs,
 Square roots and perfect squares.
 Understand the difference between the hypotenuse and the legs of a right triangle.
 Be able to identify the hypotenuse.
 Remember that the area of the square of the hypotenuse is equal to the sum of the areas formed by the other two legs,
 Square roots and perfect squares.
class notes
8_unit_1.6_notes_filled_up_2.pdf  
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more information
In other words, a PYTHAGOREAN TRIPLE fits this formula:
This, in turn, means that:
 Only TRUE RIGHT TRIANGLES can form Pythagorean Triplets
 To see if a triangle is a right triangles, its three lengths must satisfy the above formula.
 Only TRUE RIGHT TRIANGLES can form Pythagorean Triplets
 To see if a triangle is a right triangles, its three lengths must satisfy the above formula.
If what you read above seems a bit confusing, think about it this way: A PYTHAGOREAN TRIPLE is...
Here are a couple of more examples:
a list of Pythagorean triples
patterns (and tricks) to determine whether three numbers form a Pythagorean triple
 The simplest way to create further Pythagorean triples is to SCALE UP a set of triples:
is scaled up to
This means that multiples of a triple are also Pythagorean triples.
ALSO
 If the smallest number is an ODD number, the difference between the other two numbers is 1. > 3 4 5
 If the smallest number is an EVEN number, the difference between the other two numbers is 2. > 6, 8, 10
ALSO
 If the smallest number is an ODD number, the difference between the other two numbers is 1. > 3 4 5
 If the smallest number is an EVEN number, the difference between the other two numbers is 2. > 6, 8, 10
TO get the other two numbers when starting with an even number
EXAMPLES:
Let's try 6
6 / 2 = 3 3 x 3 (square) = 9 9 lies between 8 and 10 So the triple is > 6, 8, 10 Check it: (6 x 6) + (8 x 8) = (10 x 10) 36 + 64 = 100 100 = 100 
Let's try 10
10 / 2 = 5 5 x 5 = 25 25 lies between 24 and 26 So the triplet is > 10, 24, 26 Check it: (10 x 10) + (24 x 24) = (26 x 26) 100 + 576 = 676 676 = 676 
TO get the other two numbers when starting with an odd number
EXAMPLES:
Let's try 5
5 x 5 = 25 25 / 2 = 12.5 12.5 lies between 12 and 13 So the triplet is > 5, 12, 13 Check it: (5 x 5) + (12 x1 12) = (13 x 13) 25 + 144 = 169 169 = 169 
Let's try 9
9 x 9 = 81 81 / 2 = 40.5 40.5 lies between 40 and 41 So the triplet is > 9, 40, 41 Check it: (9 x 9) + (40 x 40) = (41 x 41) 81 + 1600 = 1681 1681 = 1681 
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review  workbook
math_8__unit_1.6.pdf  
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