1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Find the distance between each pair of points.
1. (8, 2) and (8, 7)‏
2. (–2, 4) and (5, 4)‏
3. (–1, –1) and (9, –1)‏
4. (–8, –4) and (–2, –4)‏
5 units
7 units
10 units
6 units

3. 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

4. Learn to use the Distance Formula and the Pythagorean Theorem and its converse to solve problems.

5. Additional Example 1: Marketing Application
What is the diagonal length of the projector screen?
Use the Pythagorean Theorem
= c2
= c2
Simplify.
58 = c2
Add.
58 = c
7.615  c
The diagonal length should be given as about 7.62 feet.

6. What is the diagonal length of the projector screen?
Check It Out: Example 1
What is the diagonal length of the projector screen?
Use the Pythagorean Theorem
= c2
12 ft
8 ft
= c2
Simplify.
208 = c2
Add.
208 = c
14.42  c
The diagonal length should be given as about 14.4 feet.

8. 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.

9. Additional Example 2A Continued
Find the distances between the points to the nearest tenth.
Substitute.
d = (0 – (–4))² + (–3 – 0 )²
Subtract.
d = (4)² + (–3)²
Simplify powers.
d =
The distance between A and B is 5 units.

10. 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.

11. Additional Example 2B Continued
Find the distances between the points to the nearest tenth.
Substitute.
d = (5 – 4)² + (–3 – 0)²
Subtract.
d = (1)² + (–3)²
Simplify powers.
d =
The distance between L and M is about 3.2 units.

12. 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.

13. Check It Out: Example 2A Continued
Find the distances between the points to the nearest tenth.
Substitute.
d = (4 – (–4))² + (0 – 0)²
Subtract.
d = (8)² + (0)²
Simplify powers.
d =
The distance between J and L is 8 units.

14. 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.

15. Check It Out: Example 2B Continued
Find the distances between the points to the nearest tenth.
Substitute.
d = ((–4) – 0)² + (– 3 – (–3)²
Subtract.
d = (–4)² + (0)²
Simplify powers.
d =
The distance between K and M is 4 units.

16. 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.
= 152
Substitute.
= 225
Simplify.
225 = 225 √
Add.
The side lengths form a right triangle.

17. 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.
= 132
Substitute.
= 169
Simplify.
163 ≠ 169 x
Add.
The side lengths do not form a right triangle.

18. 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.
= 92
Substitute.
= 81
Simplify.
61 ≠ 81 x
Add.
The side lengths do not form a right triangle.

19. 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.
= 172
Substitute.
= 289
Simplify.
289 = 289 √
Add.
The side lengths form a right triangle.

20. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 20 20

21. 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

22. 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

23. 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

24. 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 24 24

25. 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 m 25 25

26. 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 26 26