Course 3 Chapter 6 Lesson 3

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Estimate the value of the squares
roots, 1. 2. 3. 4.
5.48
3.74
7.42
6.93
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Problem of the Day The sum of the squares of two
positive numbers is 100. One number is two more
than the other. What are the numbers?
6 and 8
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Learn to use the Distance Formula and the
Pythagorean Theorem and its converse to solve
problems.
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Additional Example 1 Marketing Application
What is the diagonal length of the projector
screen?
Use the Pythagorean Theorem
72 32 c2
Simplify.
49 9 c2
58 c2
Add.
7.615 ? c
The diagonal length should be given as about 7.62
feet.
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Check It Out Example 1
What is the diagonal length of the projector
screen?
Use the Pythagorean Theorem
122 82 c2
Simplify.
144 64 c2
208 c2
Add.
14.42 ? c
The diagonal length should be given as about 14.4
feet.
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Additional Example 2A Finding Distance on the
Coordinate Plane
Find the distances between the points to the
nearest tenth.
J and K
Let A be (x1, y1)² and B be (x2, y2)².
Use the Distance Formula.
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Additional Example 2A Continued
Find the distances between the points to the
nearest tenth.
Substitute.
Subtract.
Simplify powers.
The distance between A and B is 5 units.
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Additional Example 2B Finding Distance on the
Coordinate Plane
Find the distances between the points to the
nearest tenth.
L and M
Let A be (x1, y1)² and B be (x2, y2)².
Use the Distance Formula.
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Additional Example 2B Continued
Find the distances between the points to the
nearest tenth.
Substitute.
Subtract.
Simplify powers.
The distance between L and M is about 3.2 units.
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Check It Out Example 2A
Find the distances between the points to the
nearest tenth.
J and L
Let A be (x1, y1)² and B be (x2, y2)².
Use the Distance Formula.
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Check It Out Example 2A Continued
Find the distances between the points to the
nearest tenth.
Substitute.
Subtract.
Simplify powers.
The distance between J and L is 8 units.
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Check It Out Example 2B
Find the distances between the points to the
nearest tenth.
K and M
Let A be (x1, y1)² and B be (x2, y2)².
Use the Distance Formula.
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Check It Out Example 2B Continued
Find the distances between the points to the
nearest tenth.
Substitute.
Subtract.
Simplify powers.
The distance between K and M is 4 units.
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Additional Example 3A Identifying a Right
Triangle
Tell whether the given side lengths form a right
triangle. 9, 12, 15
a2 b2 c2
Compare a² b² to c².
92 122 152
Substitute.
81 144 225
Simplify.
225 225 v
Add.
The side lengths form a right triangle.
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Additional Example 3B Identifying a Right
Triangle
Tell whether the given side lengths form a right
triangle. 8, 10, 13
a2 b2 c2
Compare a² b² to c².
82 102 132
Substitute.
63 100 169
Simplify.
163 ? 169 x
Add.
The side lengths do not form a right triangle.
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Check It Out Example 3A
Tell whether the given side lengths form a right
triangle. 5, 6, 9
a2 b2 c2
Compare a² b² to c².
52 62 92
Substitute.
25 36 81
Simplify.
61 ? 81 x
Add.
The side lengths do not form a right triangle.
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Check It Out Example 3B
Tell whether the given side lengths form a right
triangle. 8, 15, 17
a2 b2 c2
Compare a² b² to c².
82 152 172
Substitute.
64 225 289
Simplify.
289 289 v
Add.
The side lengths form a right triangle.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz Part I
Find the length of the diagonal of the rectangle.
1. width 9 in., length 40 in.
41 in.
2. base length 20 m, height 15 m.
25 m
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Lesson Quiz Part II
Find the distance between the points to the
nearest tenth.
3. Q and R
6.3
4. S and T
2.2
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Lesson Quiz Part III
Tell whether the given side lengths form a right
triangle.
5. 12 cm, 13 cm, 16 cm
no
6. 11 ft, 60 ft, 61 ft
yes
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Lesson Quiz for Student Response Systems

• 1. Find the length of the diagonal of the
  rectangle.
• width 5 m, length 12 m
• A. 8 m
• B. 11 m C. 13 m
• D. 17 m

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Lesson Quiz for Student Response Systems

• 2. Find the distance between the points to the
  nearest tenth.
• Q and S
• A. 6.0 m
• B. 6.1 m C. 7.0 m
• D. 37.1 m

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Lesson Quiz for Student Response Systems
3. Tell whether the given side lengths form a
right triangle. 12 ft, 13 ft, 14 ft A. yes B. no