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Pythagorean Theorem

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Pythagorean Theorem
Pythagorean Theorem
1. Turn your graph paper sideways or landscape. Draw a large square
on the left hand side of the paper, taking up about half of your graph
paper.
2. Label the left side as length “a”.
a
Pythagorean Theorem
3. Starting at the bottom right hand side of the square, label a point that is greater
than halfway up the side.
4. This is the length of your second square. Using that as one side, draw a second
square adjacent to the first square.
5. Label the right side as length “b”
a
b
Pythagorean Theorem
6. Along the bottom of the first square, mark off the distance that is the length of the
smaller square. Label that length as “b”.
a
b
b
Pythagorean Theorem
7. Draw a segment connecting your point to the upper left hand
corner of the large square.
8. Label BOTH sides of that segment as length “c”.
a
c
c
b
b
Pythagorean Theorem
9. Draw another segment that connects the point to the upper right
hand corner of the small square.
10. Notice the right triangle in the large square with sides a, b, and
c.
a
c
c
b
b
Pythagorean Theorem
11. You now have five different pieces.
a
c
c
b
b
Pythagorean Theorem
12. Using your scissors, cut out each piece formed.
a
c
c
b
b
Pythagorean Theorem
13. Rearrange the pieces to make a single large square with sides
of length “c”.
c
a
c
b
b
Pythagorean Theorem
c
c
Pythagorean Theorem
By rearranging the pieces to make a single large square with sides of length “c”, what
does this mean?
+
Area of square “a”
a
2
Area of square “b”
=
=
a
b
2
Area of square “c”
c
c
b
2
c
Pythagorean Theorem
Therefore,
a b c
2
2
2
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