classwork problems and homework packet - unit...

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Name___________________________________

Period____Date________________

Multi-Step EquationsDIRECTIONS: Solve each equation.NOTE: All answers hav been provided. You are responsible for

showing all the work to arrive at the correct answer listed.

1) −20 =

−4

x − 6

x

{2}

2) 6 =

1 − 2

n + 5

{0}

3)

8

x − 2 =

−9 +

7

x

{−7}

4)

a + 5 =

−5

a + 5

{0}

5)

4

m − 4 = 4

m

No solution.

6)

p − 1 =

5

p + 3

p − 8

{1}

7)

5

p − 14 =

8

p + 4

{−6}

8)

p − 4 =

−9 +

p

No solution.

9) −8 =

−(

x + 4)

{4}

10) 12 =

−4(

−6

x − 3)

{0}

11) 14 =

−(

p − 8)

{−6}

12)

−(

7 − 4

x) = 9

{4}

13)

−18 −

6

k =

6(

1 + 3

k)

{−1}

14)

5

n + 34 =

−2(

1 − 7

n)

{4}

15)

2(

4

x − 3) − 8 =

4 +

2

x

{3}

16)

3

n − 5 =

−8(

6 + 5

n)

{−1}

17)

−(

1 + 7

x) −

6(

−7 −

x) = 36

{5}

18)

−3(

4

x + 3) +

4(

6

x + 1) = 43

{4}

19)

24

a − 22 =

−4(

1 − 6

a)

No solution.

20)

−5(

1 − 5

x) +

5(

−8

x − 2) =

−4

x − 8

x

{−5}

Classwork Problems and Homework Packet - Unit 1pg. 1

Name ____________________

Period _________

Unit 1 Homework - Topic 1 & 2

Points, Lines & Planes

1. Explain the difference between COLLINEAR and COPLANAR:

Collinear:

Coplanar:

For #2 – 5, use the diagram

2. Name four points 3. Name two lines

4. Name the plane that contains points A, B, and C

5. Name the plane that contains points A, D, and E

6. Describe and correct the error in naming opposite rays in the diagram.

pg. 2

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For #7 – 10, use the diagram below

7. Give two other names for WQ 8. Give another name for plane V

9. Name three points that are collinear. Then name a fourth point that is not collinear with

these three points

10. Name a point that is not coplanar with R, S, and T

For #11 – 14, use the diagram that shows a molecule of Phosphorus Pentachloride

11. Name three points that are not collinear

12. Name two opposite rays

13. Give another name for JH

14. Name two different planes that contain HL

pg. 3

For #15 – 20, use the diagram

15. What is another name for BD? 16. What is another name for AC?

17. What is another name for ray AE? 18. Name all rays with endpoint E

19. Name two pairs of opposite rays

20. Name one pair of rays that are not opposite rays

For #21 – 28, sketch the figure described

21. Plane P and line l intersecting at one point

22. Plane K and line m intersecting at all points on line m

pg. 4

23. AB and AC 24. MN and NX

25. Plane M and NB intersecting at B 26. Plane M and NB intersecting at A

27. Plane A and plane B not intersecting 28. Plane C and plane D intersecting at XY

For #29 – 30, use the diagram.

29. Name the intersection of plane AEH and plane FBE

30. Name the intersection of plane BGF and plane HDG

pg. 5

For #31 – 36, use the diagram. Name a point that is…

31. Collinear with points E and H

32. Collinear with points B and I

33. Not collinear with points E and H 34. Not collinear with points B and I

35. Coplanar with points D, A, and B 36. Coplanar with points C, G, and F

37. Given two points on a line and a third point not on the line, is it possible to draw a plane that

includes the line and the third point? Draw a picture to explain your reasoning.

38. Is it possible for one point to be in two different planes?

Draw a picture to explain your reasoning.

39. Explain why a four-legged chair may rock from side to side even if the floor is level. Would

a three-legged chair on the same level floor rock from side to side? Why or why not?

pg. 6

40. Name two points that are collinear with P

41. Name two planes that contain J

42. Name all the points that are in more than one plane

For #43 – 46, name the geometric term modeled by the object.

43. _____________________ 44. _____________________

45. _____________________ 46. _____________________

pg. 7

Copy

right

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. All

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Practice BFor use with the lesson “Use Segments and Congruence”

Measure the length of the segment to the nearest tenth of a centimeter.

1. A B 2. M N 3. E F

Use the Segment Addition Postulate to find the indicated length.

4. Find RT. 5. Find BC. 6. Find MN.

R TS17 8.5 A CB25

54

M PN 26

32

Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent.

7. A(2, 2), B(4, 2), C(21, 21), D(21, 1); 8. M(1, 23) , N(4, 23), O(3, 4), P(4, 4);

}

AB and }CD } MN and

}OP

x

y

1

1 x

y

2

2

9. E(23, 4), F(21, 4), G(2, 4), H(21, 1); 10. R(3, 5), S(10, 5), T(24, 23), U(211, 23);

}

EG and }FH }

RS and }TU

x

y

1

1

x

y

3

3

Use the number line to find the indicated distance.

210 28 2729 26 25 24 23 22 21 0 1 2 3 4 5 6

A B C D E

11. AB 12. AD 13. CD 14. BD

15. CE 16. AE 17. BE 18. DE

Les

so

n 1

.2

Lesson

1.2

CS10_CC_G_MECR710761_C1L02PB.indd 22 4/27/11 2:32:18 PM

Unit 1 Practice - Topic 1 & 2 - Segment Addition Postulate

pg. 8

VillanovaLaw

Rectangle

Copy

right

© H

ough

ton

Miffl

in H

arco

urt P

ublis

hing

Com

pany

. All

right

s re

serv

ed.

In the diagram, points A, B, C, and D are collinear, points C, X, Y, and Z are collinear, AB 5 BC 5 CX 5 YZ, AD 5 54, XY 5 22, and XZ 5 33. Find the indicated length.

19. AB

AB

C

D

X

Y

Z

20. BD

21. CY

22. CD

23. XC

24. CZ

Find the indicated length.

25. Find ST. 26. Find AC. 27. Find NP.

32

R S T4x 12x A B C14 3x 2 4

4x 1 4

M N P3x 1 2

x 2 5

6x 2 23

Point J is between H and K on }

HK . Use the given information to write anequation in terms of x. Solve the equation. Then find HJ and JK.

28. HJ 5 2x 29. HJ 5 x }

4

JK 5 3x JK 5 3x 2 4KH 5 25 KH 5 22

30. HJ 5 5x 2 4 31. HJ 5 5x 2 3

JK 5 8x 2 10 JK 5 x 2 9

KH 5 38 KH 5 5x

32. Hiking On the map, }

AB represents a trail that you are hiking. You start from thebeginning of the trail and hike for 90 minutes at a rate of 1.4 miles per hour. Howmuch farther do you need to hike to reach the end of the trail?

1

1

A(3, 2) B(8.2, 2)

Ranger Station

Rest Area

Distance (mi)

Distance (mi)

Practice B continuedFor use with the lesson “Use Segments and Congruence”

Less

on

1.2

Lesson

1.2

CS10_CC_G_MECR710761_C1L02PB.indd 23 4/27/11 2:32:18 PM

pg. 9

Name ____________________

Period _________

Unit 1 Homework - Topic 3

Using Midpoint Formulas

For #1 – 2, find RS

1. RS = ____________ 2. RS = ____________

For #3 – 4, find x and JK

3. x = __________ JK = ____________ 4. x = __________ JK = ____________

For #5 – 6, find x and XY

5. x = __________ XY = ____________ 6. x = __________ XY = ____________

pg. 10

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For #7 – 8, the endpoints of CD are given. Find the coordinates of the midpoint M. Draw and

label the diagram, show all work.

7. C(3, −5) and D(7, 9) M = ___________

8. C(−8, −6) and D(−4, 10) M = ___________

For #9 – 11, the midpoint M and one endpoint of GH are given. Find the coordinates of the other

endpoint. Draw and label the diagram, show all work.

9. G(5, −6) and M(4, 3) H = ___________

10. H(−3, 7) and M(−2, 5) G = ___________

11. H(−2, 9) and M(8, 0) G = ___________

pg. 11

*use either method*

12. In baseball, the strike zone is the region a baseball needs to pass

through for the umpire to declare it a strike when the batter

does not swing. The top of the strike zone is a horizontal plane

passing through the midpoint of the top of the batter’s shoulders

and the top of the uniform pants when the player is in a batting

stance. Find the height of T. All heights are in inches.

T = __________

13. A house and a school are 5.7 kilometers apart on the same straight road. The library is on

the same road, halfway between the house and the school. Draw and label the diagram. How

far is the library from the house?

Distance = ___________

14. On a straight stretch of highway, a food exit is one fifth of the way between Exit 158 and

Exit 178, where the exit numbers correspond to the location in miles along the highway.

What is the exit number for the food exit?

Exit Number = _______

15. The length of XY is 24 centimeters. The midpoint of XY is M, and C is on XM so that XC is

2/3 of XM. Point D is on MY so that MD is 3/4 of MY. What is the length of CD? Draw and

label the diagram. Show all work.

CD = ________

pg. 12

Name ____________________

Period _________


Measuring & Constructing Segments (pt. 1)

For #1 – 3, find the length of the segment

1. BD

2. AC

3. ED

For #4 – 9, find the length FH

4. FH = ________ 5. FH = ________

6. FH = ________ 7. FH = ________

8. FH = ________ 9. FH = ________

pg. 13

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10. What formula can be used to find the distance between the two points, or the length of a

segment if you are given the coordinates of the endpoints?

For #11 – 15, find the distance between the two points. Show all work, including the formula.

Round to the nearest tenth if necessary.

11. A(13, 2) and B(7, 10)

Distance = _______

12. C(−6, 5) and D(−3, 1)

Distance = _______

pg. 14

13. G(−5, 4) and H(2, 6)

Distance = _______

14. R(0, 1) and S(6, 3.5)

Distance = _______

15. J(−8, 0) and K(1, 4)

Distance = _______

pg. 15

For #16 – 17, plot the points in a coordinate plane then determine whether AB and CD are

congruent. Show all work.

16. A(0, 2) B(−3, 8) C(−2, 2) D(0, −4)

LengthAB = _______

LengthCD = _______

17. A(1, 4) B(5, -1) C(−3, 1) D(1, 6)

LengthAB = _______

LengthCD = _______

pg. 16

Name ____________________

Period _________

The Pythagorean Theorem

1. What is a Pythagorean Triple?

For #2 – 5, find the value of x. Then decide whether the side lengths form a Pythagorean triple.

2. x = ___________ 3. x = ___________

Pythagorean Triple? Yes/No Pythagorean Triple? Yes/No

4. x = ___________ 5. x = ___________

Pythagorean Triple? Yes/No Pythagorean Triple? Yes/No

6. Describe and correct the error in using the Pythagorean Theorem

Unit 1 Homework - Topic 5 Supplement

pg. 17

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Rectangle

7. The fire escape forms a right triangle, as shown. Use the Pythagorean Theorem to

approximate the distance between the two platforms.

x = ___________

8. The backboard of the basketball hoop forms a right triangle with the supporting rods, as

shown. Use the Pythagorean Theorem to approximate the distance between the rods where

they meet the backboard.

x = ___________

9. You are making a kite and need to figure out how much binding to buy. You need the binding

for the perimeter of the kite. The binding comes in packages of two yards. How many

packages should you buy?

pg. 18

For #10 – 13, decide whether the triangle is a right triangle. Show all work.

10. Right Triangle? Yes/No 11. Right Triangle? Yes/No

12. Right Triangle? Yes/No 13. Right Triangle? Yes/No

For #14 – 17, verify that the segment lengths form a triangle. Then decide whether the triangle

is acute, right, or obtuse. Show all work.

14. 10, 11, and 14 15. 15, 20, and 36

Triangle? Yes/No Triangle? Yes/No

Acute/Right/Obtuse Acute/Right/Obtuse

16. 24, 30, and 6 43 17. 10, 15, and 5 13

Triangle? Yes/No Triangle? Yes/No

Acute/Right/Obtuse Acute/Right/Obtuse

pg. 19

18. In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths

form right angles. The player on first base tries to steal second base. How far does the ball

need to travel from home plate to second base to get the player out? Draw and label the

picture.

Distance = ____________

For #19 – 20, find the area of the isosceles triangle. Show all work, including formulas.

19. Area = ____________ 20. Area = ____________

21. How do you know ∠C is a right angle without using the Pythagorean Theorem?

22. Your friend claims 72 and 75 cannot be part of a Pythagorean triple because 722 + 752

does not equal a positive integer squared. Is your friend correct? Explain your reasoning

**A = 1/2 b h

pg. 20

Name ____________________

Period _________

1. In 2003, a remote controlled model airplane became the first ever to fly nonstop across the

Atlantic Ocean. The map shows the airplane’s position at three different points during its

flight. Point A represents Cape Spear, Newfoundland, point B represents the approximate

position after 1 day, and point C represents Mannin Bay, Ireland. The airplane left from Cape

Spear and landed in Mannin Bay. Show all work.

a. Find the total distance the model airplane flew.

Distance = _________________

b. The model airplane’s flight lasted nearly 38 hours. Estimate the airplane’s average speed in

miles per hour.

Average Speed = _________________

2. You travel from City A to City B. You know that the round trip distance is 647 miles. City C,

a city you pass on the way, is 27 miles from City A. Find the distance from City C to City B.

Draw and label the picture.

Distance = _________________

Unit 1 Homework - Topic 4 Additional Practice

Measuring & Constructing Segments (pt. 2)

For #1 – 3, find the length of the segment

pg. 21

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3. Your school is 20 blocks east and 12 blocks south of your house. The mall is 10 blocks north

and 7 blocks west of your house. You plan on going to the mall right after school. Find the

distance between your school and the mall assuming there is a road directly connecting the

school and the mall. One block is 0.1 mile. Draw and label the diagram. Show all work.

Distance = _________________

For #4 – 7, point S is between points R and T on RT . Use the given information to find the value

of x, RS, ST, and RT. Draw and label the diagram. Show all work.

4. RS = 2x + 10

ST = x − 4

RT = 21

x = ________

RS = _______

ST = _______

RT = _______

5. RS = 3x – 16

ST = 4x − 8

RT = 60

x = ________

RS = _______

ST = _______

RT = _______

pg. 22

6. RS = 2x − 8

ST = 11

RT = x + 10

x = ________

RS = _______

ST = _______

RT = _______

7. RS = 4x − 9

ST = 19

RT = 8x − 14

x = ________

RS = _______

ST = _______

RT = _______

8. In the diagram, AB = 1/2CD, CD = 2BC, and AD = 20 in. Find the lengths of all segments in the

diagram. Suppose you choose one of the segments at random. What is the probability that

the measure of the segment is less than 10? Show your work.

AB = ________ AC = ________

BC = ________ BD = ________

CD = ________

Probability = ________

9. Your friend claims there is an easier way to find the length of a segment than the Distance

Formula when the x-coordinates of the endpoints are equal. He claims all you have to do is

subtract the y-coordinates. Do you agree with his statement? Explain your reasoning. Include

an example.

pg. 23

10. The figure shows the position of three players during part of a water polo match. Player A

throws the ball to Player B, who then throws the ball to Player C. Show all work.

a. How far did Player A throw the ball?

Distance = _________________

b. How far did Player B throw the ball?

Distance = _________________

c. How far would Player A have to throw the ball to throw it directly to Player C?

Distance = _________________

pg. 24

11. A path goes around a triangular park, as shown.

a. Find the distance around the entire park to the nearest yard.

Distance = ____________

b. A new path and a bridge are constructed from point Q to the midpoint M of PR . Find the

coordinates of M and QM. Round to the nearest yard.

M = _____________

QM = _____________

c. A man jogs from P to Q to M to R to Q and back to P at an average speed of 150 yards

per minute. About how many minutes will it take him?

# of minutes = _____

pg. 25

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pg. 26

Unit 1 Homework - Topic 5 & 6

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Rectangle

pg. 27

Name ____________________

Period _________


Date Due _________________

Slopes of Lines

1. How are the slopes of parallel lines related? Include an example in your explanation.

2. How are the slopes of perpendicular lines related? Include an example in your explanation.

For #3 – 8, find the slope of the line that passes through the given points.

3. Slope = ____________ 4. Slope = ____________

5. Slope = ____________ 6. Slope = ____________

(−5, −1), (3, −1) (2, 1), (0, 6)

pg. 28

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7. Slope = ____________ 8. Slope = ____________

(−1, −4), (1, 2) (−7, 0), (−7, −6)

For #9 – 12, using a ruler, graph the line through the given point with the given slope.

9. P(3, −2) m = − 1/6 10. P(−4, 0) m = 5/2

11. P(0, 5) m = 2/3 12. P(2, −6) m = − 7/4

pg. 29

For #13 – 14, determine which of the lines are parallel and which of the lines are perpendicular.

13.

Parallel Lines: ________________________________________________________

Perpendicular Lines: ___________________________________________________

14.

Parallel Lines: ________________________________________________________

Perpendicular Lines: ___________________________________________________

15. Carpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof.

Slope = _________

pg. 30

16. Describe and correct the error in determining whether the lines are parallel, perpendicular,

or neither.

For #17 – 20, determine whether the lines through the given points are parallel, perpendicular,

or neither. Justify your answer.

17. Line 1: (1, 0), (7, 4) parallel/perpendicular/neither

Line 2: (7, 0), (3, 6)

18. Line 1: (−3, 1), (−7, −2) parallel/perpendicular/neither

Line 2: (2, −1), (8, 4)

19. Line 1: (−9, 3), (−5, 7) parallel/perpendicular/neither

Line 2: (−11, 6), (−7, 2)

20. Line 1: (10, 5), (−8, 9) parallel/perpendicular/neither

Line 2: (2, −4), (11, −6)

pg. 31

21. Determine whether quadrilateral JKLM is a square. Explain your reasoning.

SlopeKL = ________

SlopeLM = ________

SlopeMJ = ________

SlopeJK = ________

Square? Yes/No

Reasoning:

22. Given any 2 lines, how would you determine which line is steeper without graphing them?

Include an example in your explanation.

23. Triangle LMN has vertices L(0, 6), M(5, 8), and N(4, −1). Is the triangle a right triangle?

Explain your reasoning.

SlopeLM = ________

SlopeMN = ________

SlopeLN = ________

Right Triangle? Yes/No

Reasoning:

pg. 32

For #24 – 29, identify the slope and y-intercept of the line

Remember: put all equations into y = form first, in other words, solve for y.

24. y = 3x + 9

Slope = ____________

y-intercept = ____________

25. y = x - 7

Slope = ____________

y-intercept = ____________

26. 3x + 6y = 12

Slope = ____________

y-intercept = ____________

27. y = -x

Slope = ____________

y-intercept = ____________

28. 2y = x + 8

Slope = ____________

y-intercept = ____________

29. 2x + 3y = 5

Slope = ____________

y-intercept = ____________

pg. 33

Name ____________________ Unit 1 Homework - Topic 8

Date Due _________________ Period _________

Equations of Parallel and Perpendicular Lines

For #1 – 4, write an equation of the line passing through point P that is parallel to the given line.

Graph the equations of the lines to check that they are parallel.

1. P(0, −1) y = −2x + 3 Equation of the Line: ______________________________

2. P(3, 4) y = 1/5(x + 4) Equation of the Line: ______________________________

3. P(−2, 3) x = −5 Equation of the Line: ______________________________

pg. 34

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4. P(4, 0) −x + 2y = 12 Equation of the Line: ______________________________

For #5 – 8, write an equation of the line passing through point P that is perpendicular to the

given line. Graph the equations of the lines to check that they are perpendicular.

5. P(0, 0) y = −3x − 1 Equation of the Line: ______________________________

6. P(4, −5) y = −3 Equation of the Line: ______________________________

pg. 35

7. P(2, 3) y − 4 = −2(x + 3) Equation of the Line: _____________________________

8. P(−4, 0) 3x − 5y = 6 Equation of the Line: ______________________________

9. Describe and correct the error in writing an equation of the line that passes through the

point (3, 4) and is parallel to the line y = 2x + 1.

pg. 36

10. A new road is being constructed parallel to train tracks through point S(3, −2). The equation

of the line representing the train tracks is y = 2x. Find the equation of the line representing

the new road.

Equation of the Line: ______________________________

11. A bike path is being constructed perpendicular to Washington Boulevard through point

P(2, 2). The equation of the line representing Washington Boulevard is y = − 2/3x. Find the

equation of the line representing the bike path.


pg. 37

For #12 – 15, find the midpoint of PQ . Then write the equation of the line that passes through

the midpoint and is perpendicular to PQ .

12. P(−4, 3) Q(4, −1)


13. P(−5, −5) Q(3, 3)


pg. 38

14. P(0, 2) Q(6, −2)


15. P(−7, 0) Q(1, 8)


pg. 39

16. Write an equation of the line passing through the point (−8, 6) that is parallel to the line

y = −4x − 1


17. Write an equation of the line passing through the point (−20, 4) that is perpendicular to the

line 2x + 5y = 10


pg. 40

18. Write an equation of the line passing through the point (−8, 6) that is parallel to the line

y = −4x − 1


19. Write an equation of the line passing through the point (−20, 4) that is perpendicular to the

line 2x + 5y = 10


pg. 41

classwork problems and homework packet - unit...

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