PYTHAGOREAN
THEOREM
LISA HOLMES
Welcome to this video tutorial. Today you will be learning about the
Pythagorean Theorem.
REAL WORLD USES OF THE PYTHAGOREAN
THEOREM
• Determining what size ladder to use when painting a wall
• Finding the shortest distance when traveling
• Deciding what size television you need or want to buy
• Deciding what size computer monitor you would like to buy
• Determining arrow trajectory in archery in order to hit the target
• Designing a new staircase
Narrator will ask the questions: “How can understanding the Pythagorean
Theorem help you in your everyday life?” “What can you use it for?”
“Here are just a few examples.” Narrator will then read the list of uses of the
Pythagorean Theorem as the bullet points appear on the screen.
LEARNING OBJECTIVES
• By the end of the training video, given information on the Pythagorean
Theorem, trainees will be able to:
• Name and identify the parts of a right triangle
• Identify the algebraic equation of the Pythagorean Theorem
• By the end of the training video, given a demonstration and guided
practice, trainees will be able to:
• Solve a problem using the algebraic model of the Pythagorean
Theorem
Narrator: “What exactly will you learn from watching this video?” “Here are the
learning objectives:” Narrator will then read the objectives as they appear on
the screen.
REQUIRED SKILLS
• Before watching this video tutorial you should already have a good
understanding of:
•
Right angles
•
Basic algebra including
•
Solving algebraic equations
•
Order of operations
•
How to simplify squares
•
How to solve for square roots
Narrator: “Before moving forward with this tutorial, it is important to point out
the skills you should already have in order to successfully meet the learning
objectives of this video.” Narrator will read the prerequisite skills. “If you do not
have these skills, you may want to stop this video and review other videos that
teach these skills before moving forward.”
LEARNING OBJECTIVE 1
• By the end of the training video, given information on the Pythagorean
Theorem, trainees will be able to:
• Name and identify the parts of a right triangle
Narrator: “The first part of this tutorial will help you to name and identify the
parts of a right triangle.”
RIGHT TRIANGLE
Definition of a Right Triangle
• Right Triangle – a triangle that has a
right angle (90o)
Narrator: “The graphic shown here provides an example of what a right triangle
looks like. A right triangle is a triangle where one of the three angles is 90
degrees. A 90 degree angle is called a right angle.”
PARTS OF A RIGHT TRIANGLE
Definitions
• Leg(s) – the sides that form the
right angle (shown here in red)
• Hypotenuse – the side opposite the
right angle in a right triangle
(shown here in blue)
Narrator: “Besides the right angle, a right triangle has three main parts that you
need to become familiar with; two legs and one hypotenuse.” Narrator will then
read the definitions and point out the color coordination within the graphic.
SELF-CHECK QUESTION
Question: Is the red arrow pointing
to a leg or the hypotenuse?
Narrator: “It’s time to check your understanding. Is the red arrow in the graphic
pointing to one of the legs or at the hypotenuse? Pause the video and when you
think you have the answer, press play to see if you are correct.”
SELF-CHECK ANSWER
Answer: LEG
Narrator: “The correct answer is LEG. If you got the right answer,
Congratulations! If you did not, feel free to rewind the video to review and then
try again.”
SELF-CHECK QUESTION
Question: Is the red arrow pointing
to a leg or the hypotenuse?
Narrator: “Let’s try another one. Is the red arrow on the graphic pointing to one
of the legs or at the hypotenuse? Pause the video until you think you have the
right answer and then press play to see if you are correct.”
SELF-CHECK ANSWER
Answer: HYPOTENUSE
Narrator: “The correct answer is HYPOTENUSE. If you got the right answer,
Congratulations! If you did not, again, feel free to rewind the video to review and
then try again before moving forward.”
LEARNING OBJECTIVE 2
• By the end of the training video, given information on the Pythagorean
Theorem, trainees will be able to:
• Identify the algebraic equation of the Pythagorean Theorem
Narrator: “Now that you can name and identify the parts of a right triangle, it is
time to learn how to identify the algebraic equation of the Pythagorean
Theorem.”
ALGEBRAIC EQUATION FOR THE PYTHAGOREAN
THEOREM
Narrator: “The graphic shown displays the algebraic equation of the
Pythagorean Theorem a2+b2=c2. Notice the color coding between the
equation and the right triangle? Keep watching and you will soon understand.”
ALGEBRAIC EQUATION EXPLAINED
a2 + b 2 = c 2
• a= the length of one leg
• b= the length of the other leg
•
a and b are interchangeable; it
does not matter which leg is
labeled a and which leg is
labeled b
• c= the length of the hypotenuse
Narrator: “When solving the Pythagorean Theorem you are ultimately looking for the length of one of the sides of a
right triangle when you know the length of the other two sides. The letters in the equation (a,b and c) are specific to
the sides of the right triangle. The letter a is specific to a leg, the letter b is specific to the other leg and the letter c is
specific to the hypotenuse. It is important to know that it does not matter which leg you apply the letters a and b to;
they are interchangeable. But, the letter c is ALWAYS applied to the hypotenuse.”
SELF-CHECK QUESTION
• Label the legs of the right
triangle using a, b and/or c
• NOTE: There are two possible
correct answers
Narrator: “Lets check your understanding of the algebraic equation. Pause the
video while you attempt to label the legs of the right triangle shown in the
graphic here using the letters of the algebraic equation (a, b and/or c). Play
the video to check your answer. Need a helpful hint? There are two possible
ways to label the legs of the right triangle.”
SELF-CHECK ANSWER
Correct Answers
REMINDER: a and b
are interchangeable; it
does not matter which
leg is labeled a and
which leg is labeled b
Narrator: “The correct answers are a and b or b and a. Did you get it right?
Congratulations if you did! If you need a refresher, feel free to rewind the video
for a quick review.”
SELF-CHECK QUESTION
• Label the hypotenuse of the
right triangle using a, b,
and/or c
Narrator: “Let’s try another one. Pause the video while you attempt to label
the hypotenuse using the letters of the algebraic equation (a, b and/or c).
Press play when you are ready to check your answer.”
SELF-CHECK ANSWER
Correct Answer
The hypotenuse is always
labeled “c”
Narrator: “The answer is c. Remember, the letter c is always specific to the
hypotenuse. Now, let’s review before we move on with solving problems.”
ALGEBRAIC EQUATION REVIEW
• The algebraic equation used to solve
the Pythagorean Theorem is a2+b2=c2
• “a” represents the length of one leg
of the right triangle
• “b” represents the length of the
other leg of the right triangle
• “c” represents the length of the
hypotenuse of the right triangle
• Thus, the formula can be understood
to mean that the length of one leg
squared plus the length of the
second leg squared equals the length
of the hypotenuse squared.
Narrator: “Here are a few important things to remember regarding the
algebraic equation of the Pythagorean Theorem.” Narrator will then read the
bullet points as they appear on the screen.
LEARNING OBJECTIVE 3
• By the end of the training video, given a demonstration and guided practice,
trainees will be able to:
•
Solve a problem using the algebraic model of the Pythagorean Theorem
Narrator: “Now that you can name and identify the parts of a right triangle and
you can identify the algebraic equation of the Pythagorean Theorem, it is time
to solve a problem using the algebraic model of the Pythagorean Theorem.”
ALGEBRAIC MODEL
DEMONSTRATION
Steps:
•
•
•
Solve for the hypotenuse:
Begin with the equation
Plug in the values for a, b, and c based on
the graphic shown (a=3, b=4, c=?)
•
•
•
𝑐2 = 25
Solve the equation
•
The narrator will verbally walk the trainee
thru the steps provided as they appear on
the screen, pausing at each step.
25=c2
Simplify the equation by finding the square
root of both sides of the equal sign
•
•
9+16=c2
Add the values
•
•
(3) 2=9 and (4) 2=16
By simplifying, the equation becomes:
•
•
(3) 2+(4) 2=c2
Solve the squares to simplify:
•
•
a2+b2=c2
c=5
Answer: The length of the hypotenuse is 5
Steps:
SELF-CHECK
(PAUSE AT EACH STEP TO TEST YOUR
KNOWLEDGE)
•
Begin with the equation
•
•
Solve for the hypotenuse:
Plug in the values for a, b, and c based on the
graphic shown (a=5, b=12, c=?)
•
•
•
𝑐2 = 169
Solve the equation
•
Narrator will walk trainee thru each step.
Narrator will ask the trainee to pause the
video at each step.
169=c2
Simplify the equation by finding the square root
of both sides of the equal sign
•
•
25+144=c2
Add the values
•
•
(5) 2=25 and (12) 2=144
By simplifying, the equation becomes:
•
•
(5) 2+(12) 2=c2
Solve the squares to simplify:
•
•
a2+b2=c2
c = 13
Answer: The length of the hypotenuse is 13
END OF TUTORIAL
• Thank you for viewing this video tutorial about the Pythagorean Theorem.
• View more video tutorials at www.mathtube.com
Narrator: “Congratulations! You’ve completed this video tutorial about the
Pythagorean Theorem. Feel free to watch it again if you need to or find more
math tutorial videos at www.mathtube.com”