Classroom notes regarding everything you need to know about Pythagoras and his famous theorem.

1. Pythagoras and his Theorem
Pythagoras of Samos
a short history
Pythagoras is arguably one of
the most important
mathematicians of his time.
He was born in 569 BCE on
the small Greek island,
Samos. During his life, he
perfected his method of
traveling education, where he
taught in Middle-Eastern
cities.
!
Many people of the time could
not follow the intricate math
theroems, and unfortunately
thought that Pythagoras was
crazy! Even if some
questioned his sanity,
Pythagoras attracted like-minded
individuals where they
continued to learn his
teachings in secret as to not
Name: Date:! ! ! ! Class:
Lingley 8 Math
be considered evil. This secret
group called themselves The
Pythagoreans. Their
meetings became so secret,
that they developed their
own language, and
even had their own
seal, etched above
the doors where their
meetings were held.
The Pythagoreans thought
that all problems could be
solved by numbers. This must
be how they discovered how
to correctly build their iconic
Greek columns. Before news
of Pytagoras’ Theorem
spread, all buildings were
formed with crooked bottoms,
since there was no tool of
measurement to ensure that
their bases were straight.
!
The Pythagoreans traveled
throughout Greece with their
special measurement tool: the
12 knot rope. With this they
were able to solve many
building mistakes.

2. x x ✓
Lingley 8 Math
Solving the Theorem
If
only these columns
were straight!
Understanding the Pythagorean Theorem
Pythagoras saw that the crooked columns casted a triangular
shadow on the ground. Using his knowledge of geometry, he
saw that the crooked columns casted an acute triangle. He then
discovered that the only triangle that will work with his theorem is
a right angle triangle.
hypotenuse
leg
right angle
isosceles acute right
Once Pythagoras switched to only using the right angle
triangle, he soon found a relationship between the legs on
either side of the right angle, and the hypotenuse.
The Secrets behind the Theorem
1. Squares can be formed around each side of the triangle.
2. The sum of the small and medium square areas’ equals the area
around the hypotenuse.
3. This relationship is only true for right angle triangles.
4. The theorem is used when solving for an unknown length of a
triangle.
5. The theorem will also work for any regular polygon around the sides of
the triangle.

3. Example 1
36 cm2
Lingley 8 Math
Applying the Theorem
Using the Pythagorean Theorem, find the
value of the hypotenuse.
6 cm
8 cm
h
h
8 cm
8 cm
6 cm
h
6 cm
1. Draw squares around all sides of the right
angle triangle, and label them.
2. Find the areas of each of those squares.
+ 64 cm2 = 100 cm2
6 cm
6 cm
8 cm
8 cm
3. We now know that the area of the purple
square is 100 cm2. However this is only
the area! We now need to take the
square root to find the side length!
4. Take the square root of the hypotenuse √100 cm2 = 10 cm
Final Answer!
Using the Pythagorean Theorem, find the missing values of the triangles below.
Your Turn!
4 cm
4 cm
h
5 cm
10 cm
h
6 cm
x
9 cm
Do your work on the next page.
If you find the area is a non-square... approximate!

4. Lingley 8 Math
Do your work here!