GRADE 8 ALGEBRA

THE PYTHAGOREAN

THEOREM

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.

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. 

INTRODUCTION

Visit the site for information on Pythagoras: http://www.worldbookonline.com/student/article?id=ar453500&st=pythagoras

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.

Task #1

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 squaresStep 3: Solve the equationRemember- a diagonal is the same

as a hypotenuse

www.ixl.com/math/grade-8/pythagorean-theorem-find-the-length-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.

 

a2+b2  = c2

TASK #4Remember, 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?