(8) Lesson 5.5 - The Pythagorean Theorem

1. Course 3, Lesson 5-5
Use the look for a pattern strategy to solve Exercises 1–3.
1. In a stadium, there are 10 seats in the 1st row, 13 seats in the 2nd row,
16 seats in the 3rd row, and so on. How many seats are in the 10th row?
2. Find the next three numbers in the sequence
20, 24, 21, 25, 22, 26, ... .
3. Sarah rents videos from a video rental store that charges a monthly rate
of $9.95 plus $0.75 per video rental. If Sarah’s total monthly bill was
$30.95, how many videos did she rent?
4. The Ito family is driving to Oklahoma from Texas. If they average 65
miles per hour, how far will they drive in hours?
1
3
2

2. Course 3, Lesson 5-5
ANSWERS
1. 37 seats
2. 23, 27, 24
3. 28
4. 227.5 miles

3. HOW can algebraic concepts be
applied to geometry?
Geometry
Course 3, Lesson 5-5

4. Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• 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.EE.2
Use square root and cube root symbols to represent solutions to
equations of the form x2 = p and x3 = p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots
of small perfect cubes. Know that 2 is irrational.

5. Course 3, Lesson 5-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

6. To
• find the missing side length of a right
triangle by using the Pythagorean
Theorem,
• determine whether a triangle is a right
triangle by using the converse of the
Pythagorean Theorem
Course 3, Lesson 5-5
Geometry

7. • legs
• hypotenuse
• Pythagorean Theorem
• converse
Course 3, Lesson 5-5
Geometry

8. Course 3, Lesson 5-5
Geometry
Words In a right triangle, the sum of the squares of the lengths of
the legs is equal to the square of the length of the
hypotenuse.
Model
Symbols 2 2 2
a b c 

9. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Write an equation you could use to find the
length of the missing side of the right triangle.
Then find the missing length. Round to the
nearest tenth if necessary.
Check:
Pythagorean Theorema2 + b2 = c2
Replace a with 12 and b with 9.
144 + 81 = c2
The equation has two solutions, 15 and –15. However, the length of a side
must be positive. So, the hypotenuse is 15 inches long.
122 + 92 = c2
Evaluate 122 and 92.
225 = c2 Add 81 and 144.
Definition of square root
c = 15 or –15 Simplify.
a2 + b2 = c2
122 + 92 = 152
144 + 81 = 225
225 = 225
?
?
±√225 = c

10. Answer
Need Another Example?
Write an equation you could use to find the
length of the missing side of the right triangle
shown. Then find the missing length. Round to
the nearest tenth if necessary.
122 + 162 = c2; 20 in.

11. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
2. Write an equation you could use to find the length
of the missing side of the right triangle. Then find
the missing length. Round to the nearest tenth if
necessary.
Check for
Reasonableness
Pythagorean Theorema2 + b2 = c2
Replace a with 8 and c with 24.
64 + b2 = 576
The length of side b is about 22.6 meters.
82 + b2 = 242
Evaluate 82 and 242.
64 – 64 + b2 = 576 – 64 Subtract 64 from each side.
Definition of square root
b2 = 512 Simplify.
The hypotenuse is always the longest side in
a right triangle. Since 22.6 is less than 24,
the answer is reasonable.
7
b ≈ 22.6 or –22.6 Use a calculator.
b = ±√512

12. Answer
Need Another Example?
Write an equation you
could use to find the length
of the missing side of the right
triangle shown. Then find the missing length.
Round to the nearest tenth if necessary.
a2 + 282 = 332; 17.5 in.

13. Course 3, Lesson 5-5
Geometry
If the sides of a triangle have lengths a, b, and c units such that
, then the triangle is a right triangle.2 2 2
a b c 

14. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. The measures of three sides of a triangle are
5 inches, 12 inches, and 13 inches. Determine
whether the triangle is a right triangle.
Pythagorean Theorema2 + b2 = c2
a = 5, b = 12, c = 13
25 + 144 = 169
The triangle is a right triangle.
52 + 122 = 132
Evaluate 52, 122, and 132.
169 = 169 Simplify.
?
?

15. Answer
Need Another Example?
The measures of three sides of a
triangle are 24 inches, 7 inches, and
25 inches. Determine whether the
triangle is a right triangle.
yes; 72 + 242 = 252

16. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-5
Geometry

17. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-5
Geometry
Sample answers:
• An algebraic formula is used to find the missing side
length of a right triangle.
• You solve a square root equation to find the missing
side length of a right triangle.

18. Determine whether a
triangle with side lengths of
1 centimeter, 2 centimeters,
and 3 centimeters is a right
triangle. Justify your
response.
Ratios and Proportional RelationshipsFunctionsGeometry
Course 3, Lesson 5-5