Transcript Pythagorean Theorem - Sage Middle School

Pythagorean Theorem
By now you are able to find the area of a triangle,
surface area of a triangle and the volume of a
triangular prism. All of these formulas deal with the
space of a triangle, but what about the sides.
The Pythagorean Theorem allows you to find any of
the given sides of a right triangle. Thinking back to
our angle unit a right triangle is a triangle with a 90
degree angle.
Pythagorean Theorem Continued
• The Pythagorean Theorem comes to us from
the Greeks. Credit is given to a man named
Pythagoras (570 BC – 495 BC.) It is possible
that he wasn’t the one who actually came up
with the formula.
a + b = c
So where is it used?
• The Pythagorean Theorem is used anytime you
know two sides of a triangle but not the third.
Some examples are pitching a tent and needing
to know how long a rope needs to be to tie it to
the ground. Another example might be archery
when trying to make an up hill shot. Perhaps you
are building a house and need to figure out how
long the trusses need to be.
a + b = c
How do you use it.
a +b=c
4 + 6 = c
16 + 36 = 52
c=
52
Where does it come from
• As you can see the area of the square labeled see is
the size of a and b added. This is where the formula
comes from.
What is the square root of 52?
• Remember that when we take a number to the second
power we have multiplied that number by itself. The
inverse of taking a number to a power is to find the
root of the result. Therefore what two numbers
multiplied by each other result in 52.
In this case we know that it would be between 7 and 8,
because 7 X 7 =49 and 8 X 8 = 64.
Challenge keep trying numbers between 7 and 8 to see if
you can find an exact answer, or is the answer irrational
such as the square root of 2?
Application
• Last week you began building a floor plan. This
week I would like you to design your roof. Using the
Pythagorean theorem please design a roof system
for your house.
• What will the total cost be of the roof. Don’t worry
about staying in your budget for this one.