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Unit 2 – Geometry – Lesson 4 – The Pythagorean Theorem
Essential Questions:
1. Explain the history of Pythagoras and his most famous theory, “The Pythagorean Theorem.”
2. How can I use the Pythagorean Theorem to decide if three lengths would form a right triangle?
3. How can I use the Pythagorean Theorem to find an unknown length in a right triangle?
Think about It!
What type of angles do you think ancient civilizations were concerned about? Why?
_________________ __________________
Right Angles:

Because all buildings were built with right angles to ensure stability, studies of right angles date
back as far as _______________ BC (3,110 years ago).
The first study…

The first study of right angles was by ancient _______________________________.

They were interested in forming right angles at corners of ___________________ and other
buildings.

The Egyptians discovered that a triangle with sides of ______, _____, and _____ formed a 90
degree angle.
The Egyptian’s 3, 4, 5:

The Egyptians did not use or discover the Pythagorean Theorem.

They just knew that _________________ right triangle existed.

They knew that a ___, ___, ___ triangle formed a 90 degree angle.
The Egyptian’s 3, 4, 5:

To make sure they had 90 degree corners in their buildings, they used a ___________ (made of
horse hair) with __________ evenly spaced knots.

This understanding of 3, 4, 5 triangles is what
allowed the Egyptians to build _______ corners in
their buildings and pyramids and is the
basis for why we can still view them today.
The Chinese:

People believe that the Chinese knew about the Egyptian’s 3, 4, 5 triangle theory.

A clay tablet of Babylonian origin was found with the following inscription: “4 is the length and
5 is the diagonal. What is the breadth?”
Answer: ______________________________
What did Pythagoras Find?

Pythagoras found that not only triangles with sides 3, 4, and 5 make right angles, but
_____________________ ____________ __________________________ make right angles.

There is __________________ ____________ ___________ way to make a right triangle!

He found that any triangle has a right angle if “When the two shorter sides in a right triangle are
squared and then added, the sum equals the square of the longest side or hypotenuse.”
What does this mean?
How did Pythagoras prove his theory?

He proved it _______________ different ways!!!!

Why?
o He proved it 84 ways because _______________________________________________
_______________________________________________________________________
Skill #1:

Use the Pythagorean Theorem to decide if three lengths would create a right triangle.
1. Label the legs “a” and “b”; label the _______________________ (the longest side) “c.”
2. Test a2+b2 to see if it equals c2.

If yes, then it ___________________________________________________

If no, then it ____________________________________________________
Test it!
1. Would a triangle with sides of 5, 7, and 10 be a
right triangle?
2. Would a triangle with sides of 8, 15, and 10
have a right angle? Why or why not?
Does a2+b2 = c2?
Does a2+b2 = c2?
Skill #2:

Use the Pythagorean Theorem to calculate a missing measurement.
1. Label the legs “a” and “b”; label the _______________________ (the longest side) “c.”
2. Substitute your _____________ values for a, b, and/or c.
3. Leave the variable for your __________________ measurement.
4. Solve the equation by using inverse operations.
 **Steps will vary whether you are finding the smallest, medium, or longest side
of the triangle**
Practice:
Find the length of the longest side (the
Hypotenuse)
Find the length of the shortest side (a)
Find the length of the medium side (b)
Find the length of the hypotenuse in a triangle
with coordinates (-5, 0), (-5, 6), and (0, 6) to the
nearest tenth.
2 Step Problem:

Use the Pythagorean Theorem to find the height of the triangle. Then find the area of the
triangle.
Review: The Pythagorean Theorem
In Words
Numbers
Algebra
32 + 42 = 52
a2 + b2 = c2
In any right triangle, the sum of
the square of the _________ is
equal to the square of the
______________________.
9 + 16 = 25
Reflection:
1. Can you explain the history of the Pythagorean Theorem?
yes
or
yes
or
no
3. Can you calculate the length of the hypotenuse given the legs of the triangle?
yes
or
no
4. Can you calculate the length of the legs given the hypotenuse of the triangle?
yes
or
no
5. Do you want to meet with Mrs. Daniel during study hall about this lesson? yes
or
no
2. Can you state the Pythagorean Theorem equation?
no
Practice Problems:
Would a triangle with sides of 8, 15, and 17 be a
right triangle?
What is the length of the hypotenuse of a triangle
if the legs are 5 and 12?
Would a triangle with sides of 7, 11, and 8 be a
right triangle? **Be sure to label a, b, and c**
If a triangle has a leg length of 6 and a hypotenuse
of 10, what is the length of the medium length leg
of the triangle?