Pythagoras Print Activity

Use the Video Interactive to answer all of the following questions:

1. a. What variables represent the 3 sides of the right triangle? ______, ______, ______

b. What variables represent the 2 sides that make up the right angle? ______, ______

c. What variable represents the longest side called the hypotenuse? ______

d. From the following list, circle the shape of the colored area that sits on each side of the triangle.

Circle / Rectangle / Square / Rhombus

2. Read the instructions to answer each of the following questions.

a. Move slider a to 3.

What value appears inside the blue square on side a of the triangle? What is the area of the blue square on side a? ______This relationship can be written as 32  .

b. Move slider b to 4.

What value appears inside the red square on side b of the triangle?

What is the area of the red square on side b? ______This relationship can be written as 42  .

c. When slider a is 3 and slider b is 4:

What value appears inside the green square on side c of the triangle? What value appears outside the green square on side c? The area of the green square can be written as 52 = .

Junior High Math Interactives Page 1 of 4 2005 Alberta Education (www.LearnAlberta.ca)

Shape and Space / Pythagoras / Video Interactive / Print Activity

d. Complete the following statement that defines the Pythagorean Theorem:

The square of the length of side ___ plus the square of the length of side ___ equals the square of the length side ___ .

e. Write your statement from above using the variables a, b, and c:

___2 + ___2 = ___2

f. Write your statement from above using the values a = 3, b = 4, and c = 5:

___2 + ___2 = ___2

3. Move slider a to 8 and slider b to 6.

a. How many squares are on side a? _____

b. How many squares are on side b? _____

c. Together the number of squares on sides a and b equal the number of squares on side c. So side c has _____ squares.

d. Use the values obtained above to complete the following statements: a 2  b 2  c 2 ____ 2  ____ 2  c 2

____ ____  ____

e. The Pythagorean Theorem is used to find the length of side c if you know the lengths of sides a and b. In the Video Interactive, what mathematical operation is used in the second last step to change c 2 to c?

______

4. Given the following values for a and b, determine the length of side c, to 2 decimal places,

a. If a = 5 and b = 8, b. If a = 7 and b = 4, a 2  b 2  c 2 a 2  b 2  c 2 ____ 2  ____ 2  c 2 ____ 2  ____ 2  c 2 _____ _____  c 2 _____ _____  c 2

_____  c 2 _____  c 2 _____  c _____  c = c 2 = c 2 ____ 2  ____ 2  c2 ____ 2  ____ 2  c2 _____ _____  c 2 _____ _____  c 2 _____  c 2 _____  c 2 _____  c _____  c

c. If a = 5 and b = 5, d. If a = 2 and b = 10, a 2  b 2  c 2 a 2  b 2  c 2 ____ 2  ____ 2  c 2 ____ 2  ____ 2  c 2 _____ _____  c 2 _____ _____  c 2

_____  c 2 _____  c 2 _____  c _____  c

= c 2 = c 2 ____ 2  ____ 2  c2 ____ 2  ____ 2  c2 _____ _____  c 2 _____ _____  c 2 _____  c 2 _____  c 2 _____  c _____  c

5. A student performed the following steps using the Pythagorean Theorem. Circle the step where the student made an error and write the corrected solution (including all steps) to the right of the student’s work. Use the following example to help you answer the upcoming questions.

Eg: If a = 4 and b = 6 Corrected Solution: 42  62  c 2 42  62  c 2 8 12  c 2 16  36  c 2 20  c 2 52  c 2 20  c 2 52  c 2 4.47  c 7.21  c

*Refer to example on previous page.

a. If a = 5 and b = 8 Corrected Solution:

a2 + b2 = c2 52  82  c 2 13  c 2 13  c 2 3.61  c

b. If a = 2 and b = 9 Corrected Solution:

a2 + b2 = c2 22  92  c 2 4 18  c 2 22  c 2 22  c 2 4.69  c

c. If a = 3 and b = 6 Corrected Solution:

a2 + b2 = c2 32  62  c 2 9  36  c 2 45  c 2 45  c 2 45  c

d. If a = 10 and b = 10 Corrected Solution:

a2 + b2 = c2 102 102  c 2 10 10  c 2 20  c 2 13  c 2 10  c