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The Pythagorean theorem

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by

Kate Ficarra

on 26 June 2017

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Transcript of The Pythagorean theorem

The Pythagorean theorem
For right triangles
a + b = c
Where a, b and c are legs and c is the hypotenuse.
We will use the Pythagorean theorem to find missing side lengths
If the missing side is a leg
If the missing side is the hypotenuse
2
2
2
Step 1 -
Step 2 -
Step 3 -
Step 4 -
Identify a, b and c
Plug a, b and c into Pythagorean Theorem
Simplify equation
Solve for missing value
1.
Label a, b, c
Write Pythagorean theorem
Substitute a, b and c
Simplify exponents
Add !
Take square root of both sides
Simplify if needed
2.
3.
4.
5.
6.
7.
Label a, b, c
Write Pythagorean theorem
Substitute a, b and c
Simplify exponents
Take square root of both sides
Simplify if needed
Subtract !
1.
2.
3.
4.
5.
6.
7.
18
15
10
8
In a right triangle, the sum of the squares of the legs has a special relationship with the square of the hypotenuse. What is this relationship?
Investigation
A long time ago in a land
far far away...

Your best guess about a
mathematical relationship.

It is usually a generalization about a
pattern
you think might be true, but that you do not yet know for sure is true.
Conjecture
The sum of the square of the legs of a right triangle

equals
the square of the hypotenuse.
Let's get Conjectural
a
b
c
a
b
c
=
+
2
2
2
Where is the
Hippos home?
label the hypotenuse with the letter c
How can we correct the Scarecrow’s statement so it is mathematically precise?
Can you correct the Scarecrow?
Full transcript