Colorful Playful Illustrative Pythagorean Theorem Education Presentation

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THE PYTHAGOREAN
THEOREM
THE PYTHAGOREAN
THEOREM
Define the Pythagorean Theorem1
Define a right triangle2
Identify real-life applications4
Apply the Pythagorean Theorem3
LEARNING TARGETS
The Pythagorean Theorem
states that, in a right triangle,
the square of the hypotenuse
is equal to the sum of the
squares of the legs.
INTRODUCTION
HISTORY
The ancient Greek mathematician and
philosopher Pythagoras is credited with
discovering this relationship in the 6th
century BCE due to the prominence of
his religious-mathematical school in
Croton, Italy.
That said, It was likely independently
discovered in several different cultures.
There is evidence of its use in Egypt,
Babylon, and China as far back as the
20th century BCE.
The Pythagorean Theorem has been
proved through hundred of
methods and new proofs are still
being discovered.
Here is an example of a visual proof
showing the squares of the sides.
Notice, 9 + 16 = 25!
VISUAL PROOFS
9
16
25
UNDERSTANDING
RIGHT TRIANGLES
h
yp
o
te
nu
se
leg
le
g
A right triangle is any triangle with one right angle. 
The two sides that form the right angle are called the
legs. The side opposite the right angle is called the
hypotenuse. 
A right angle creates many special relationships
between the sides and angles of the triangle and is
the basis of the mathematical branch of
trigonometry. 
Determine which side
you are trying to find. 
Identify the two legs of
the triangle and the
hypotenuse. 
Note their lengths.
Substitute your lengths
into the Pythagorean
Theorem equation and
solve for the missing
value. 
1 2 3
USING THE PYTHAGOREAN THEOREM
leg
hypotenuse
leg
USING THE PYTHAGOREAN THEOREM
1
Identify the two legs
of the triangle and
the hypotenuse. 
Note their lengths.
8 in
15 in
?
USING THE PYTHAGOREAN THEOREM
Determine which
side you are
trying to find. 
2
2
a = 8 in
b = 15 in
USING THE PYTHAGOREAN THEOREM
Substitute your
lengths into the
Pythagorean Theorem
equation and solve for
the missing value. 
c = ? 8 + 15 = c 2 2 2
64 + 225 = c 2
289 = c 2
17 = c 
3
Building and
architecture
1
Navigation
and GPS
2
Games and
sports
3
REAL LIFE APPLICATIONS
The Pythagorean Theorem describes the
relationship between the sides of a right triangle.
SUMMARY
It can be used to find the missing side of a right triangle,
which can be applied to solve many real-life problems.
Understanding the Pythagorean Theorem is a great foundation
for learning trigonometry, the distance formula, and more!
What other examples can you think
of for using the Pythagorean
Theorem in your life?
What other examples can you think
of for using the Pythagorean
Theorem in your life?