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Pythagorean
Theorem
Obj: SWBAT identify and apply the
Pythagorean Thm and its converse to
find missing sides and prove triangles
are right
Standard: M11.C.1.4.1 Find the
measure of a side of a right triangle
using the Pythagorean Thm
History of the Pythagorean Thm

At the height of their power, nearly a
millennium before Pythagoras, circa 1900 1600 BCE , the Babylonians (Babylon
located in modern day Iraq) identify what
are now called Pythagorean triples (a set
of positive integers a, b, c such that a2 +
b2 = c2
History of the Pythagorean Thm

A Chinese astronomical and
mathematical treatise called
the Chou Pei Suan Ching
(The Arithmetical Classic of
the Gnomon and the
Circular Paths of Heaven,
ca. 500-200 B.C.), possibly
predating Pythagoras, gives
a statement of and
geometrical demonstration
of the Pythagorean Thm.
History of the Pythagorean Thm

Despite evidence
predating him, the
Greek named
Pythagoras is credited
with the theorem.
According to tradition,
Pythagoras once said,
“Number rules the
universe…” WHAT A
FREAKING GENIUS!!!!
Basics of the Right Triangle
hypotenuse
leg
leg
Right angle
Pythagorean Thm


In ANY right triangle, the sum of the
squares of the lengths of the legs is equal
to the square of the length of the
hypotenuse.
a2 + b 2 = c 2
Use the Pythagorean Thm to solve
for x.
x
3
4
1. Square both legs
1
2
3
4
5
6
7
8
9
10 11
12 4 ft
13
14 15
4ft
16
3 ft
1
2
3
4
5
6
7
8
9
3 ft
2. Count the total squares
1
2
3
4
5
6
7
8
9
10 11
12 4 ft
13
14 15
4ft
16
9 + 16 = 25
3 ft
1
2
3
4
5
6
7
8
9
3 ft
3. Put that number of squares on
the hypotenuse 21
16
1
5
9
13
22
11 17 23
24
6 12 18
7 13 19
25
1
2 3 4
8
14
20
2
3
15
6 7 8
9
4
10
10 11 12 4
5
ft
14 15 16
3
4ft
1 ft2
3
9 + 16 = 25
4
5
6
7
8
9
3 ft
4. Count the number of squares that
touch the hypotenuse. 21
16
1
5
9
13
22
11 17 23
24
6 12 18
7 13 19
25
1
2 3 4
8
14
20
2
3
15
6 7 8
9
4
10
10 11 12 4
5
ft
14 15 16
3
4ft
1 ft2
3
9 + 16 = 25
#=5
4
5
6
7
8
9
3 ft
5.That number is the length of the
hypotenuse. 21
16
1
5
9
13
22
11 17 23
24
6 12 18
7 13 19
25
1
2 3 4
8
14
20
2
3
15
6 7 8
9
4
10
10 11 12 4
5
ft
14 15 16
3
#=5
4ft
1 ft2
3
Length = 5
9 + 16 = 25
4
5
6
7
8
9
3 ft
LOOK
FAMILIAR?!
WOW, it’s
actually the
Pythagorean
Thm! That’s
so freaking
cool!!!
Why are
the wrong
answers
wrong???
Pythagorean Triples


Are short cuts! They are sets of 3 whole
numbers (a, b, and c) that satisfy the
equation a2 + b2 = c2
Most frequent examples:




*** 3, 4, 5 (where a=3, b=4, c=5) ***
5, 12, 13
8, 15, 17
7, 24, 25
ANY scale or multiple of Pythagorean triples will
work!!!
Pythagorean Triple Example
Don’t be
fooled by
the
disguise…
...it’s still the
Pythagorean
Thm!!
Pythagorean Thm application with
even more Geometry!!! It’s actually
that much more fun!!!
HOLY SMOKES, LOOK AT ALL OF
THIS GEOMETRY!!! A-MAZ-ING!!!!