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Practice BFor use with the lesson “Prove Theorems about Perpendicular Lines”
What can you conclude from the given information? State the reason for your conclusion.
1. ∠1 > ∠ 2 2. n ⊥ m 3. ###$ BA ⊥ ###$ BC
r
s1 2
m
n1 2
4 3
12
AB
C
Find the value of x.
4.
(x 1 25)8
z 5.
(2x 2 11)8518
6.
2x8 x8
7.
(x 2 15)8
8.
(3x 1 6)8
9. (x 2 15)8
(x 1 5)8
Find the measure of the indicated angle.
608
1
265
34
10. ∠1 11. ∠ 2
12. ∠ 3 13. ∠ 4
14. ∠ 5 15. ∠ 6
In Exercises 16–18, use the diagram. r s t
m
n
16. Is r i s?
17. Is m i n?
18. Is s i t?
Name ——————————————————————— Date ————————————
Less
on
3.6
GeometryChapter Resource Book 3-79
Lesson
3.6
CS10_CC_G_MECR710761_C3L06PB.indd 79 4/27/11 2:48:10 PM
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Find the distance from point A to line c. Round your answers to the nearest tenth.
19.
x
y
1
1
A
c
20.
x
y
1
1
A
c
21.
x
y
1
1
A
c
22.
x
y
1
1
Ac
23.
x
y
1
1
A
c
24.
x
y
1
1
A
c
25. Maps A map of a neighborhood is drawn on a graph where units are measured in feet.
100
300
500
700
100 300 500 700 900
P
a b
26381
c d e
a. Find m∠1.
b. Find m∠ 2.
c. Find the distance from point P to line a.
d. Find the distance from point P to line c. Round your answer to the nearest foot.
Practice B continuedFor use with the lesson “Prove Theorems about Perpendicular Lines”
Name ——————————————————————— Date ————————————
Les
so
n 3
.6
GeometryChapter Resource Book3-80
Lesson
3.6
CS10_CC_G_MECR710761_C3L06PB.indd 80 4/27/11 2:48:11 PM
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Lesson Write and Graph Equations of Lines, continued
9. a. AE Þ DB b. 2 A
} B 5 2 D
} E , B Þ 0, E Þ 0
10. a. Your loan: y 5 112 2 8x; the slope is 28 and represents paying your sister $8 per week; the y-intercept is 112 and represents the initial amount of the loan.
Your brother’s loan: y 5 165 2 13.75x; the slope is 213.75 and represents paying your sister $13.75 per week; the y-intercept is 165 and represents the initial amount of the loan.
b.
0 4 82 6 10 120
255075
100125150175
y
x
Number of weeks
Am
ou
nt
ow
ed(d
olla
rs)
14
Your brother will pay off his loan first. From the graph, the x-intercepts of both linear equations represent when you and your brother will pay off your loans. The x-intercept of the linear equation that represents your brother’s loan is 12 and the x-intercept of the linear equation that represents your loan is 14. So, your brother will pay off his loan in 12 weeks and you will pay off your loan in 14 weeks. c. You can determine who will pay off the loan first by algebraically determining the x-intercept of each equation. d. The intersection of the two lines represents when you and your brother will owe your sister the same amount of money. e. Yes. After the third week, you have paid your sister $24 and therefore you have to pay her $88 more. Because you now want to pay $11 a week, the equation that represents your loan is now y 5 88 2 11x. It will take you 8 weeks to pay back $88. So, it will take you a total of 11 weeks to pay off your loan, and you will pay off your loan first.
Lesson Prove Theorems about Perpendicular LinesTeaching Guide
1. the distance between two points in a coordinate plane; the coordinates of points; dis-tance formulas: d 5 Ï
}}
(x2 2 x1)2 1 ( y2 2 y1)2
2. The sum of their measures is 908; the sum of their measures is 1808; no, they can be adjacent or nonadjacent angles. 3. a line that intersects two or more coplanar lines at different points; corresponding, alternate interior, alternate exterior, and consecutive interior angles are formed; corresponding, alternate interior, and alternate exterior angles are congruent, consecutive interior angles are supplementary
Investigating Geometry Activity
1. Yes, because all of the angles formed by their intersection were right angles.
2. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
3. They are parallel, because the corresponding angles, alternate interior angles, and alternate exterior angles are congruent.
4. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Practice Level A
1. Theorem 9 2. Theorem 8
3. Theorem 10 4. 458 5. 308 6. 158 7. 908
8. 608 9. 308 10. 408 11. 458 12. 458
13. 408 14. 458 15. 508 16. yes 17. yes
18. no 19. 35 20. 40 21. 30 22. D
23. a. 700 ft b. 500 ft c. 783 ft d. no
Practice Level B
1. r ⊥ s; Theorem 8 2. ∠1, ∠ 2, ∠ 3, and ∠ 4 are right angles; Theorem 9 3. ∠1 and ∠ 2 are complementary; Theorem 10 4. 65 5. 25
6. 30 7. 105 8. 28 9. 50 10. 908 11. 308
12. 608 13. 308 14. 308 15. 608 16. no
17. yes 18. yes 19. 2.8 20. 4.2 21. 4.5
22. 3.2 23. 3.6 24. 4.5 25. a. 908 b. 278
c. 500 ft d. 224 ft
Practice Level C
1. 588 2. 168 3. 908 4. 258 5. 528 6. 258
7. 258 8. 658 9. 658 10. no 11. no 12. yes
13. 15 14. 18 15. 21 16. 20 17. 12 18. 15
19. 4.9 20. 3.6 21. 6 22. 5.8
23. a. 0.7 mi b. 1.4 mi c. Even though the highway is closer, it would be shorter (1.4 miles) for the lost hikers to walk to the hiking trail than to the highway because the river is between the
an
sw
er
s
GeometryChapter Resource BookA42
3.5
3.6
