PythagoreanTheoremActivitiesV2 M3 03 Pythagorean Theorem Activities V2

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Pythagorean Theorem Activities: 7th and 8th Grade

(leg1)2 + (leg2)2 = hypotenuse2
Standard: MG3.3 Know and understand the Pythagorean theorem and its converse and use it to
find the length of the missing side of a right triangle and the lengths of other line segments and,
in some situations, empirically verify the Pythagorean theorem by direct measurement.

Materials: Handouts, centimeter ruler, chalk and a measuring tape for each student

Debrief Warm - Up (handout and answer key included):

One Minute Math History of Pythagoras (optional):
Thousands of years ago, in the 6th century BCE in Greece,
Pythagoras was the leader of a kind of math and philosophy
religious movement. Pythagoras is famous for the Pythagorean
Theorem named after him which states that for right triangles,
a 2 + b 2 = c 2 . This means that if you square the lengths of the
smaller two sides of a right triangle and add those values together,
you get the square of the length of the longest side. Long before
Pythagoras lived, people in Babylonia (in present-day Iraq) and in
India knew about that pattern in right triangles and had been using
it for centuries, but Pythagoras is credited with proving it.

Pythagorean Triples (handout included - print in high quality):
Split the class into four groups. Each student will have their own half sheet to fill out. Three of
the sheets will have a different Pythagorean triple on grid paper and questions, while the other
will not be a right triangle and will not work. After a few minutes to complete, ask students from
each group to share out the relationship they have discovered.
Discuss: This is an informal proof that the Pythagorean Theorem works for any right triangle but
does not work for other triangles.

MCC@WCCUSD
(M3)
10/19/11

Notes:
Example 1: We can use the Pythagorean Theorem (leg1)2 + (leg2)2 = hypotenuse2 or
a 2 + b 2 = c 2 to find the missing side of a right triangle.
Use your ruler to draw a rectangle to scale, that has legs of length 7 cm by 10 cm.
Next draw a diagonal through the rectangle.

7 cm

10 cm

What two shapes do you now have?
Do you know all the lengths of the right triangle?
What is the missing side? a, b or c?
Draw the right triangle and label the sides.

[2 congruent right triangles]
[No]
[c, the hypotenuse]

10
cm

7 cm
c

Since we have a right triangle and one missing side, we can use the Pythagorean Theorem to find
the hypotenuse. Round to the nearest tenth because we are finding a length.

a 2 + b 2 = c 2 where a = 7 , b = 10 and c is unknown.
7 2 + 10 2 = c 2
49 + 100 = c 2
149 = c 2
149 = c 2
c ≈ 12.2
Take your ruler and measure the length to see how accurate we are.

MCC@WCCUSD
(M3)
03/05/13

You Try: Make a rectangle with dimensions 5 cm by 9 cm. Find the length of the diagonal of the
rectangle. Round your answer to the nearest tenth and check the length by measuring with a
ruler.

a 2 + b 2 = c 2 where a = 5 , b = 9 and c is unknown.
52 + 92 = c 2
25 + 81 = c 2
106 = c 2
106 = c 2
c ≈ 10.3

Small Group Activity/Formative Assessment:
The converse of the Pythagorean Theorem states that a triangle has to be a right triangle if
a 2 + b 2 = c 2 is true. In groups of three, you will be using measuring tapes to draw right triangles
on the ground outside with chalk. Your group will decide the leg lengths of your right triangle
and you’ll use a 2 + b 2 = c 2 to find the hypotenuse. If your group finishes early, make your right
triangle into a rectangle by constructing a congruent right triangle. Demonstrate inside.
Questions/prompts for students during outside activity:
Did you start at zero on the tape measure?
(Many students struggle with measuring and will need review or individual help.)
What side lengths did you choose?
Show your steps with good syntax, equal signs lined up.
How did you find the hypotenuse?
Double check each measurement.
Who will be explaining your work to the other groups?
How will you explain this work to other groups?
Gallery Walk for Student Talk: One student stays with each triangle or rectangle, others rotate
to see and discuss successful examples.

Extension/Homework: CST released item:
In this figure, AB and CD are perpendicular.
What is the perimeter of ΔABC ?

MCC@WCCUSD
(M3)
03/05/13

Warm-Up

Name:

CST/CAHSEE:
If x = 100 , what is the value of 3 x ?

Review:
40 is between which two integers on a number
line? Explain to your math partner how you can tell.

A) 13
B) 30
C) 300
D) 310

• What possible mistake was made to get the
other incorrect answers?

Current:

Other:
Explain the difference between the answers to

100 and x 2 = 100 .
8m
17 m

What is the length of x?
A) 8 m
B) 15 m
C) 19 m
D) 25 m
•

Use process of elimination and what you know about
triangles to figure out the answer above. Explain your
thinking.

Today’s Objective/Standards: Know the Pythagorean Theorem and compute the length of an unknown side. 7MG 3.3

MCC@WCCUSD
(M3)
03/05/13

Warm-Up

Name:

CST/CAHSEE:
If x = 100 , what is the value of 3 x ?
We
are
going
to
evaluate
for
x
equals
what
number,
class?
[100]

A) 13
B) 30

= 3 100

C) 300

= 3 10 • 10

100 is
what
number
times
itself?
[10]
The
square
root
of

= 3 • 10

10 2 is?
[10]

D) 310

•

= 30

What possible
mistake was made to get the

other incorrect

answers?

A) added
10 & 3

B) multiplied
10 & 3

Review:
40 is between which two integers on a number
line? Explain to your math partner how you can tell.

40 is
between
6
and
7
because

36 < 40 < 49
and
simplified
it's

6 <

40 < 7 .

C) Put 3 & 10
together

Current:

Other:
Explain the difference between the answers to

100 and x 2 = 100 .
8m
17 m

What is the length of x?
A) 8 m
B) 15 m
C) 19 m
D) 25 m
•

Since we are just beginning our study of
the Pythagorean Theorem, you may have
answered this by eliminating answer
choices bigger than 17 since the longest
side of a right triangle is the hypotenuse
and it is 17 m. The other sides are called
legs and they are not equal lengths, so it
must be 15 m.

100 = 10 , this is the principal square root, so you
simplify it.
Whereas, x 2 = 100 is solving an equation.

(10)(10) = 100 and (− 10)(− 10) = 100, so
x = 10,−10
For our lesson today, we will be using the principal
square root to find the length of a side of a triangle
because length is represented as a positive number.

Use process of elimination and what you know about
triangles to figure out the answer above. Explain your
thinking.
Today’s Objective/Standards: Know the Pythagorean Theorem and compute the length of an unknown side. 7MG 3.3

MCC@WCCUSD
(M3)
03/05/13

Name:
Fill out this sheet and be ready to report back to the class.
What are the lengths of the legs of the right triangle?
What is the length of the hypotenuse?
What are the areas of the squares off of the legs?
What is the sum of those two areas?
What is the area of the square off of the hypotenuse?
Explain the relationship between the sum of the areas off of the legs and area off of the hypotenuse?

Do you think all right triangles will have lengths that are integers? Explain.

Name:
Fill out this sheet and be ready to report back to the class.

What are the lengths of the legs of the right triangle?
What is the length of the hypotenuse?
What are the areas of the squares off of the legs?
What is the sum of those two areas?
What is the area of the square off of the hypotenuse?
Explain the relationship between the sum of the areas off of the legs and area off of the hypotenuse?

Do you think all right triangles will have lengths that are integers? Explain.

MCC@WCCUSD
(M3)
03/05/13

Name:
Fill out this sheet and be ready to report back to the class.

Do you think all right triangles will have lengths that are integers? Explain.

MCC@WCCUSD
(M3)
03/05/13

Do you think all right triangles will have lengths that are integers? Explain.

MCC@WCCUSD
(M3)
03/05/13

Name:
Fill out this sheet and be ready to report back to the class.
What are the lengths of the shorter sides of the triangle? ___________
What is the length of the longest side? _______________________
What are the areas of the squares off of the shorter sides?
What is the sum of those two areas?
What is the area of the square off of the longest side?
Explain the relationship between the sum of the areas off of the shorter sides and the area off of the
longest side. ________________________________________________________________________
___________________________________________________________________________________
If there is no relationship, why do you think that is? _________________________________________
___________________________________________________________________________________

Name:

_______________________

Fill out this sheet and be ready to report back to the class.
What are the lengths of the shorter sides of the triangle? ___________
What is the length of the longest side? _______________________
What are the areas of the squares off of the shorter sides?
What is the sum of those two areas?
What is the area of the square off of the longest side?
Explain the relationship between the sum of the areas off of the shorter sides and the area off of the
longest side. ________________________________________________________________________
___________________________________________________________________________________
If there is no relationship, why do you think that is? _________________________________________
___________________________________________________________________________________
MCC@WCCUSD
(M3)
03/05/13

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Page Count                      : 9
Title                           : PythagoreanTheoremActivitiesV2
Author                          : Philip Gonsalves
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Create Date                     : 2013:03:06 05:06:45Z
Modify Date                     : 2013:03:06 05:06:45Z
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