Transcript THE PYTHAGOREAN THEOREM - St. Francis Cathedral School

THE PYTHAGOREAN
THEOREM
GRADE 8 ALGEBRA
WELCOME
In this Web-Quest you
will learn a little about
Pythagoras and what he
contributed to our
world. You will also
review the Pythagorean
Theorem and discover
its applications for real
life. You need to
complete a few tasks.
You will complete each
task on separately. At
the conclusion of the
Web Quest you will
hand in all the
required work
together.
INTRODUCTION
Fiona is locked in the
house and is
calling Shrek to save
her. It is
difficult for Shrek to
save her as the only open
window is on the second
floor. In order to save
Fiona, Shrek has to
borrow a ladder from
one of his neighbors.
You need to help Shrek
save Fiona by calculating
the length of the
ladder he needs to
reach the window and
complete his mission.
Task #1
Shrek heard about a
person named
Pythagoras who might be
able to help. Your first
task is to follow the site
at the right and find out
about Pythagoras. After
doing the research you
need to answer the
questions found in
worksheet #1 at the end
of this presentation.
Remember to write your
findings separately
labeled Task #1.
Visit the site for information on Pythagoras:
http://www.worldbookonline.com/student/arti
cle?id=ar453500&st=pythagoras
Task #2
You have learned
the Pythagorean
Theorem. Your next
task is to practice
what you have
learned. Review the
steps to solving the
theorem. Then, go to
the site provided.
You will be given on
line problems.
Copy the
problems first.
Then, solve it
showing all work.
Use the site to find
your mistakes.
Step 1: a2 + b2 = c2 where a and b are
the legs and c is the hypotenuse
Step 2: Substitute the given values
Step 2: Simplify squares
Step 3: Solve the equation
Remember- a diagonal is the same as
a hypotenuse
www.ixl.com/math/grade8/pythagorean-theorem-find-thelength-of-the-hypotenuse
Task #3
Now apply what
you have learned
from this lesson by
working Task #3
Worksheet
attached below
which contains
real life situations
that need to be
solved by using
the Pythagoras
Theorem.
Process
Remember, Pythagoras
Theorem is only used with
Right Angled Triangles.
The sum of the squares of
the sides of a right angled
triangle is equal to the
square of the length of the
hypotenuse
Now using the knowledge you
have learned on Pythagoras
Theorem, you are able to
help Shrek in saving Fiona.
2
2
a +b
=
2
c
TASK #4
Remember, Shrek needed to
get to the second floor. It is
9.5 meters above ground.
Because of the bush outside
the house Shrek needs to
place the ladder 3 meters
away from the house. He goes
around the neighborhood to
find a ladder that will reach
Fiona. How long does the
ladder need to be to help save
Fiona? Show all work.
Oops! Since you and Shrek
had work to accomplish that
took some time, the
groundskeeper cut the bush
and built a shed outside the
window. The shed now gets
in the way. Shrek needs to
place the ladder 4.5 meters
from the house. This changes
the length of the ladder Shrek
needs. What is the length of
the ladder required now?
Evaluation:
You will be assessed on all four tasks. You need to submit each task
separately. Each task should be clearly labeled.
In Task #1 each question should be written and answered in complete
sentences.
In Task #2 each problem should be explained using the format for
proofs. All work should be shown and answers clearly marked.
In Task #3 all problems should be clearly defined. You need to draw a
diagram, a right triangle, to model the problem. Label all sides that are
given. All work should be explained using the format for proofs.
In Task #4 show all work using format for proofs. All work should be
shown and answers clearly marked.
Task #1
After reading the article answer these questions briefly.
1) About where and when was he born?
2) Pythagoras was a Greek philosopher and mathematician. What was his
greatest contribution to the math world?
3) As a philosopher, Pythagoras taught about the transmigration of the soul.
Explain what that means.
4) As a scientist Pythagoras applied his theories to Copernican theory of the
universe. What did that state?
5) Why were the people of Crotona suspicious of the Pythagorean
brotherhood? What happened as a result?
TASK # 3 Number the problems, 1-6. Be sure to show your work. Draw your own
graphic to help explain the problems.
1) To get from point A to point B you must avoid walking through a pond. You must
walk 34 meters south and 41 meters east. To the nearest meter, how many meters
would be saved if it were possible to walk through the pond?
2) A baseball diamond is a square with sides of 90 feet. What is the shortest
distance, to the nearest tenth of a foot, between first base and third base?
3) A suitcase measures 24 inches long and 18 inches high. What is the diagonal
length of the suitcase to the nearest tenth of a foot?
4) The older floppy diskettes measured 5 and 1/4 inches on each side. What
was the diagonal length of the diskette to the nearest tenth of an inch?
5) Two joggers run 8 miles north and then 5 miles west. What is the shortest
distance, to the nearest tenth of a mile, they must travel to return to their
starting point?
6) Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet
long and the bottom of the house is 6 feet across. What is the height of his dog
house, in feet, at its tallest point?