THE PYTHAGOREAN
THEOREM
LEARNING TARGETS
1 Define the Pythagorean
2 Theorem
Define a right triangle
3 Apply the Pythagorean
4 Theorem
Identify real-life
applications
INTRODUCTION
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.
HISTORY
The ancient Greek mathematician That said, It was likely
and philosopher Pythagoras is independently discovered in
credited with discovering this several different cultures. There
relationship in the 6th century is evidence of its use in Egypt,
BCE due to the prominence of his Babylon, and China as far back as
religious-mathematical school in the 20th century BCE.
Croton, Italy.
VISUAL PROOFS
The Pythagorean Theorem has 16
been proved through hundred
of methods and new proofs
are still being discovered. 9
Here is an example of a visual 25
proof showing the squares of
the sides. Notice, 9 + 16 = 25!
UNDERSTANDING
RIGHT TRIANGLES
se
nu
A right triangle is any triangle with one right
te
angle.
po
leg
hy
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
leg relationships between the sides and angles
of the triangle and is the basis of the
mathematical branch of trigonometry.
USING THE PYTHAGOREAN THEOREM
1 2 3
Identify the two Determine which Substitute your
legs of the triangle side you are trying lengths into the
and the to find. Pythagorean
hypotenuse. Theorem equation
Note their lengths. and solve for the
missing value.
USING THE PYTHAGOREAN THEOREM
hypotenuse
1
Identify the two leg
legs of the
triangle and the
hypotenuse.
Note their
lengths.
leg
USING THE PYTHAGOREAN THEOREM
2 ?
Determine 8 in
which side you
are trying to
find.
15 in
USING THE PYTHAGOREAN THEOREM
a = 8 in
3 b = 15 in
Substitute your c=? 82 + 152 = c 2
lengths into the 2
Pythagorean 64 + 225 = c
2
Theorem equation
2
and solve for the 289 = c
missing value.
17 = c
REAL LIFE APPLICATIONS
1 2 3
Building and Navigation Games and
architecture and GPS sports
SUMMARY
The Pythagorean Theorem describes the
relationship between the sides of a right
triangle.
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?
