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 | |
File Size: | 4100 kb |
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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 |
Videos that may help
online interactive activities
worksheets
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review - workbook
math_8_-_unit_1.6.pdf | |
File Size: | 3284 kb |
File Type: |