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Pythagorean theoremStations Review

Ideas for Implementation: Stations are excellent for classroom practice. Students can work in groups to discuss and practice their knowledge of the Pythagorean theorem. Students should not write on the station cards but on their recording sheets.

Teacher Tips: Print on cardstock or laminate to keep station cards lasting.

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8.6C Use models and diagrams to explain the Pythagorean theorem

8.7C Use the Pythagorean theorem and its converse to solve problems.

8.7D Determine the distance between two points on a coordinate plane using the Pythagorean theorem.

8.G.6 Explain a proof of the Pythagorean theorem and its converse.

8.G.7 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.8 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Students will be able to use the Pythagorean theorem to find missing side lengths of right triangles and to problem solve in two dimensions, three dimensions and on a coordinate plane.

Use the word bank to fill in each of the blanks in the paragraph below.

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The Pythagorean ______________ tells us how the side lengths

of ______________ triangles are related. In any right triangle,

the ______________ of the squares of the two ______________

should equal the ______________ of the hypotenuse. The legs

are called ______________ and ______________, and the

hypotenuse is ______________. The ______________ is always

the longest side of a right triangle, and its across from the

______________ angle.

theorem

right

sumlegs

squarea

bc

hypotenuse90°

1

2

3 4

5

6 7

8 9

10

Find the missing side length of each right triangle. Round to the nearest tenth when necessary.

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1. 2. 3.

4. 5. 6.

24

45

?36

85

?

11

12

?

20

13?

30

16?

40

30 ?

Prob

lem

1. 2. 3.

Wor

k

72 + 242 = c2

49 + 576 = c2

625 = c2

c = 625

122 + 132 = c2

144 + 169 = c2

313 = c2

c = 17.7

152 + 362 = c2

30 + 72 = c2

102 = c2

c = 10.1

solu

tion The missing side length

is 625 units.

The missing side length

is 17.7 units.

The missing side length

is 10.1 units.

In each of the three problems below, a mistake was made when trying to find the missing length of the right triangle. Find and explain the

mistake in the work, and then correct the solution.

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7

24

?12

13? 36

15

?

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State whether each description of a triangle is a right triangle or not. Justify your answers.

1. Veronica cut a triangular piece of

cookie cake with side lengths that measure

3.6 cm, 6 cm and 4.8 cm.

2. The table top of a side table is triangular

shaped with side lengths of 12 inches, 22.5 inches and 25.5

inches.

3. Tony uses a triangular shaped guitar

pick. It’s side lengths measure 3.5 cm, 4 cm

and 3.5 cm.

4. A bird left its post and flew in a triangular path. It

flew 21 yards south, 72 yards east and 75 yards diagonally to end back at

the post.

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Using a pencil and a paper clip, spin both spinners. Plot the two points on the coordinate plane, and find the distance between

the two points.

(-4, -3) (-1, -4)

(-2, 3)

(-1, -5)

(-3, 3)

(1, 5) (3, 4)

(2, -2)

(3, 5)

(4, -1)

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A city has plans to build a park that will be shaped like the trapezoid below. Each unit on the graph represents 100 feet. Use the graph to

answer questions 1-3.

●

● ●

●

1. The city plans to build a fence around the park. How

many total feet of fencing will they need?

2. If fencing costs $7 per foot, what will the total cost of

fencing be?

3. The city plans to plant a tree every 4 feet around the perimeter of the park. How many trees will they need to

plant?

Find x, the diagonal distance inside each rectangular prism below. Round answers to the nearest tenth.

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1. 2.

3. 4.

8 feet6 feet

7 feetx

16 inches

12 in

12 inx

40 cm30 cm

20 cmx

4 feet2 feet

8 feetx

1. Mrs. Greever has four square desks pushed together as shown. She wants to tape a diagonal “x” on the top of each desk, because the desks are broken. How many total feet of tape will she need? Round to the nearest whole number.

2. Max’s house has two steps on the front porch as shown. If each step is the same size, what is the total vertical distance covered by the two steps?

3. Georgia bought a snow cone shaped like the cone below. What is the height of the snow cone?

6 in.

10 in.

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Use the Pythagorean theorem to help you solve each of the following problems.

6 feet

6 in.

5 in.

Name___________________________________________ Date ___________________________________ Pd _____

Station 1:

1. ______________________ 6. ______________________

2. ______________________ 7. ______________________

3. ______________________ 8. ______________________

4. ______________________ 9. ______________________

5. ______________________ 10. ______________________

Station 2:

1. _____________________

2. _____________________

3. _____________________

4. _____________________

5. _____________________

6. _____________________

Station 3:1. Mistake: _______________________________________________________

Correction: ____________________________________________________

2. Mistake: _______________________________________________________

Correction:____________________________________________________

3. Mistake: _______________________________________________________

Correction:____________________________________________________

Station 4:

1. ___________________________

______________________________

2. ___________________________

______________________________

3. ___________________________

______________________________

4. ___________________________

______________________________

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Unit: Pythagorean TheoremStations Review

Pythagorean theorem

Station 5:

Station 6:

1. _____________________

2. _____________________

3. _____________________

Station 7:

1. _____________________

2. _____________________

3. _____________________

4. _____________________

Station 8:

1. _____________________

2. _____________________

3. _____________________

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Point 1: _________

Point 2: _________

Distance: _______

Point 1: _________

Point 2: _________

Distance: _______

Point 1: _________

Point 2: _________

Distance: _______

Station 1:

1. ______________________ 6. ______________________

2. ______________________ 7. ______________________

3. ______________________ 8. ______________________

4. ______________________ 9. ______________________

5. ______________________ 10. ______________________

Station 2:

1. _____________________

2. _____________________

3. _____________________

4. _____________________

5. _____________________

6. _____________________

Station 3:1. Mistake: _______________________________________________________

Correction: ____________________________________________________

2. Mistake: _______________________________________________________

Correction:____________________________________________________

3. Mistake: _______________________________________________________

Correction:____________________________________________________

Station 4:

1. ___________________________

______________________________

2. ___________________________

______________________________

3. ___________________________

______________________________

4. ___________________________

______________________________

Name___________________________________________ Date ___________________________________ Pd _____

©Maneuvering the Middle, 2016

Unit: Pythagorean TheoremStations Review

Pythagorean theorem

Answer Key

Theorem

right

sum

legs

square

a

b

c

hypotenuse

90°

51

77

16.3

15.2

34

26.5

The square root was not taken at the last step.

The missing side length is 25 units.

The formula was set up to solve for c, but a leg is missing.

The missing side length is 5 units.

The legs were multiplied by two instead of squared.

The missing side length is 39 units.

Yes; 3.62 + 4.82 = 62

Yes; 122 + 22.52 = 25.52

No; 3.52 + 3.52 ≠ 42

Yes; 212 + 722 = 752

Station 5:

Station 6:

1. _____________________

2. _____________________

3. _____________________

Station 7:

1. _____________________

2. _____________________

3. _____________________

4. _____________________

Station 8:

1. _____________________

2. _____________________

3. _____________________

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Point 1: _________

Point 2: _________

Distance: _______

Point 1: _________

Point 2: _________

Distance: _______

Point 1: _________

Point 2: _________

Distance: _______

*Student answers will vary based on each spin.

4,400 feet

$30,800

1,100 trees

12.2 feet

23.3 inches

53.9 centimeters

9.2 feet

34 feet

16 inches

4 inches