MCRBG-0102-PA.qxd 4-27-2001 9:57 AM Page 27 1.2 N Practice...

Decide whether the statement is true or false.

1. Point X lies on . 2. X, W, and Z are collinear.

3. Point W lies on . 4. X, W, and Z are coplanar.

5. and are collinear. 6. and are coplanar.

7. and are collinear. 8. and are coplanar.

Name a point that is collinear with the given points.

9. B and E 10. C and H

11. D and G 12. A and C

13. H and E 14. G and B

15. B and I 16. B and C

Name a point that is coplanar with the given points.

17. M, N, and R 18. M, N, and O

19. M, T, and Q 20. Q, T, and R

21. T, R, and S 22. Q, S, and O

23. O, P, and M 24. O, S, and R

Complete the sentence.

25. consists of the endpoints A and B and all points on the line that lie

26. consists of the initial point P and all points on the line that lie

27. Two rays or segments are collinear if they

28. and are opposite rays if

Sketch the figure described.

29. Three points that are coplanar but not collinear.

30. Three lines that intersect at a single point.

31. A set of three lines that has two points of intersection.

32. A set of three lines that has three points of intersection.

33. Two planes that intersect.

34. Two planes that do not intersect.

35. Two rays that intersect at their initial points.

36. Two rays that do not intersect.

? .→ML

→MN

? .

? .↔PQ

→PQ

? .↔ABAB

M

N

O

P Q

R

S

T

A B C

D E F

G HI

→YV

→YX

→YV

→YX

→YV

→YW

→YV

→YW

VYY

ZV

WX

m

→ZY

Geometry 27Chapter 1 Resource Book

Copyright © McDougal Littell Inc. All rights reserved.

Practice BFor use with pages 10–16

1.2LESSON

Lesson

1.2

NAME _________________________________________________________ DATE ___________

MCRBG-0102-PA.qxd 4-27-2001 9:57 AM Page 27



NAME DATE


1.3LESSON

Lesson

1.3

Use a ruler to measure the length of each line segment to the

nearest millimeter.

1. 2. 3.

Draw a sketch of the three collinear points. Then write the

Segment Addition Postulate for the points.

4. A is between T and Q. 5. M is between H and A.

6. J is between S and H. 7. A is between L and B.

In Exercises 8–11, use the following information.

S is between T and V. R is between S and T. T is between R and Q. and Make a sketch and answer the following.

8. Find RS. 9. Find QS. 10. Find TS. 11. Find TV.

Suppose J is between H and K. Use the Segment Addition

Postulate to solve for x. Then find the length of each segment.

12. 13. 14.

Find the distance between each pair of points.

15. 16. 17.

18. Marathon The map at the right is being used to plan a 26.3 mile marathon. Coordinates are given in miles. The locations of theparticipating towns on the map are: Curtis Clearfield Buster and Angel City

Which of the following planned routes is nearest to the 26.3 milerequirement?

(a) Curtis to Clearfield to Angel City to Curtis(b) Curtis to Clearfield to Buster to Angel City to Curtis(c) Curtis to Buster to Clearfield to Curtis(d) Curtis to Buster to Angel City to Clearfield to Curtis

�1, 4�.�5, 7�,�10, 2�,�0, 0�,

x

y

2

2

4

4

6

6

8 10

8

10

Buster

Angel City

Curtis

Clearfield

x

y

1

1

A(3, 2)

B(2, 0)

C(1, �3)

x

y

2

2

G(�1, 0)

I(1, 3)

H(2, �4)

x

y

2

2

E(�2, 4)D(1, 3)

F(0, �4)

A�3, 2�, B�2, 0�, C�1, �3�G��1, 0�, H�2, �4�, I�1, 3�D�1, 3�, E��2, 4�, F�0, �4�

KH � 12x � 4KH � 131KH � 22

JK � 5x �23JK � 8x � 9JK � 3x � 3

HJ � 2x �13HJ � 5x � 3HJ � 2x � 4

TR � RS � SV.QT � 6,QV � 18,

E

F

CDA

B




1.3 Challenge: Skills and ApplicationsFor use with pages 17–25

LESSONNAME _________________________________________________________ DATE ___________

Lesson

1.3

1. Suppose Use the Segment Addition Postulateto show that

2. Suppose and What other segments must be congruent? (Use the Segment AdditionPostulate.)

In Exercises 3 and 4, consider the following statement.

If A, B, and C are collinear points, then

3. Explain how the statement differs from the first half of the SegmentAddition Postulate.

4. Sketch a counterexample to show that the statement is false.

In Exercises 5–7, let A, B, C, and D be four points in a plane. Tell

whether the given condition is sufficient to conclude that

Justify your answer by using the Segment

Addition Postulate or by sketching a counterexample.

5. B is between A and C, and B is between A and D.

6. B is between A and D, and C is between B and D.

7. B and C are both between A and D.

In Exercises 8–10, assume that K is between J and L.

8. If and find x. (Hint: Make sure your answer is reasonable!)

9. If and find x.

10. If the ratio of KL to JK is 2:7, and find JK.

In Exercises 11–13, use the following information to determine

whether

In a three-dimensional coordinate system, the distance between two pointsand is

.

11. 12. 13.

R�0, �4, 4�R�1, �7, 9�R�5, 0, 4�Q�2, �4, �1�Q��1, �4, 4�Q�2, 5, 6�P�1, 0, �3�P��4, 1, 2�P�3, 7, �2�

��x2 � x1�2 � �y2 � y1�2 � �z2 � z1�2

�x2, y2, z2��x1, y1, z1�

PQ � QR.

JL � 162,

JL � 10,JK � 20 � x2, KL � 2 � x,

JL � x2,JK � 2x � 5, KL � 5x � 3,

AB � BC � CD � AD.

AB � BC � AC.

U V W X Y ZVW � XY.UV � WX � YZ

LR � MS. L M R SLM � RS.

MCRBG-0103-CS.qxd 4-27-2001 9:56 AM Page 47



Lesson

1.4

NAME DATE

Practice CFor use with pages 26–32

1.4LESSON

Use a protractor to measure each angle to the nearest degree.

Write two names for each angle.

1. 2. 3.

Use the Angle Addition Postulate to find the measure of the

unknown angle.

4. 5. 6.

In a coordinate plane, plot the points and sketch Classify the

angle. Write the coordinates of a point that lies in the interior of the

angle and the coordinates of a point that lies in the exterior of the

angle.

7. 8. 9.

In Exercises 10–13, use the following information.

Q is in the interior of S is in the interior of P is in the interior ofand

Make a sketch and answer the following.

10. Find 11. Find 12. Find 13. Find

Let Q be in the interior of Use the Angle Addition Postulate

to solve for x. Find the measure of each angle.

14. 15. 16.

m�POR � �5x � 1��m�POR � 61�m�POR � 26�

m�QOR � �2x �43��m�QOR � �5x � 2��m�QOR � �2x � 2��

m�POQ � �13x �

13��m�POQ � �3x � 7��m�POQ � �x � 4��

�POR.

m�SOPm�ROQm�QOTm�QOP

m�ROQ � m�QOS � m�POT.m�SOT � 71�,m�ROT � 127�,�SOT.�QOP.�ROS.

C��7, �2�C�4, 2�C�1, �4�B��2, �4�B��1, �4�B��3, 0�A�0, 1�A��5, 0�A��5, �4�

�ABC.

X

W

Z

Y

32�

25�

E

D

C

F

48�82�

A

D

C

F23�

21�

m�XYZ � ? m�CDE � ? m�FDC � ?

A C

U

M

T

Q

K

J

L

MCRBG-0104-PA.qxd 5-2-2001 4:14 PM Page 55

60 GeometryChapter 1 Resource Book



LESSONNAME _________________________________________________________ DATE ___________

Less

on

1.4

1. Suppose Use the Angle Addition Postulate toshow that

2. Suppose and Use the AngleAddition Postulate to write as many additional pairs of congruent angles as possible.

In Exercises 3–6, use the diagram shown.

3. If andfind x.

4. If andfind x. (Hint: Make sure your

answer is reasonable!)

5. If and find

6. If the ratio of to is 5:3, and find

In Exercises 7 and 8, consider the following statement.

If and are adjacent angles, then

7. Explain how the statement differs from the Angle Addition Postulate.

8. Sketch a counterexample to show that the statement is false.

In Exercises 9–11, assume that and are adjacent angles, and

assume that

9. If is acute, write an expression for in terms of x.

10. If is obtuse, write an expression for in terms of x.

11. If is a right angle, which of your two expressions gives in terms of x?Explain.

m�RST�RSP

m�RST�RSP

m�RST�RSP

m�RSP � m�PST � x�.�PST�RSP

m�RSP � m�PST � m�RST.�PST�RSP

m�LJM.m�KJM � 144�,m�LJMm�KJL

m�KJL.m�KJM � 140�,3�m�LJM� � 2�m�KJL�

m�LJM � �x2 � 1��,m�KJL � 85�,m�KJM � �2x2 � 6x � 5��,

m�LJM � �3x � 10��,m�KJL � 6x�,m�KJM � 145�,

�RXT � �UXW.�2 � �4

�BAD � �CAE.�1 � �3. A

BC D

E

1 2 3

X

R

ST

U

1 2 34

5

V

W

J

K

L

M




NAME DATE


1.5LESSON

Less

on

1.5

Use a ruler to measure and redraw the line segment on a piece of

paper. Then use construction tools to find the segment bisector.

1.

2.

Find the coordinates of the midpoint of a segment with the given endpoints.

3. 4. 5.

Find the coordinates of the other endpoint of the segment with the

given endpoint and midpoint M.

6. 7. 8.

Use a protractor to measure and redraw the angle on a piece of

paper. Then use construction tools to find the angle bisector.

9. 10. 11.

is the angle bisector of Find the two angle measures

not given in the diagram.

12. 13. 14.

bisects Find the value of x.

15. 16. 17.

(4x � 63)�

(15x � 25)�A

B

C

T

(5x � 28)�

(12x � 7)�

A

B

C

T(5x � 7)�

(3x � 13)�

A

B

C

T

�ABC.→BT

R

T

42�P

S

R

ST

44�

PR

T

37�

PS

�RPS.→PT

R

DM

A

M

T

M

G

T

M�2, 1�M��1, �1�M�2, 0�P�7, 3�A��4, 3�T�6, 2�

F��3, �5�D�6, 3�B�5, �1�E�5, 0�C��4, �3�A��3, 5�

T W

A B





LESSONNAME _________________________________________________________ DATE ___________

In Exercises 1–4, is the midpoint of both and

1. If and find x.

2. If and find x.

3. Can you be certain that Explain.

4. If and what are the possible values of x?

5. Let be an angle, and let M be the midpoint of

Can you conclude that bisects If so, explain why. Ifnot, sketch a counterexample.

6. Suppose bisects bisects bisects What is the maximum possible measure of

7. Suppose bisects and bisects If find bothpossible measures of Sketch both possible situations.

8. Suppose and bisects What is Sketch this situation.

In Exercises 9–14, use the following information to find the midpoint of

If and are two points in a three-dimensional coordinate system,

then the midpoint of has coordinates

9. 10. 11.

12. 13. 14.

Q�1.6, �2.4, 1.9�Q�6.2, �4.6, 0.3�Q�8, �5, 12�P�12, 35, 8.7�P�3.4, 1.8, 3.9�P�2, 0, 7�Q��11, 6, 3�Q�2, 6, �2�Q�3, 7, 11�P��3, 2, 7�P�2, 0, 8�P�5, 7, �5�

�x2 � x1

2,

y2 � y1

2,

z2 � z1

2 �.AB

B�x2, y2, z2�A�x1, y1, z1�

PQ.

M

m�AXB?�AXB.

→XD�AXB � �BXC � �CXD ��DXE ��EXA,

�JPK.m�JPM � 150�,�KPM.

→PL�JPL

→PK

�BAC?�BAF.�BAE,

→AE�BAD,

→AD

→AC

�PQR?→QM

PR.�PQR

DE � x2,AB � 2x � 3

AB � DE?

AE � x2 � 2,AC � 2x � 1

CD � x � 2,BC � x2 � 18

BD.AEC A B C D E

Q

M

P

R

Less

on

1.5




NAME DATE

Practice AFor use with pages 44–50

1.6LESSON

Use the figure at the right.

1. Are and adjacent?

2. Are and a linear pair?

3. Are and a linear pair?

4. Are and vertical angles?



Use the figure at the right.

7. If then

8. If then

9. If then

10. If then

11. If then

12. If then

In Exercises 13–16, assume and are complementary and

and are supplementary.

13. If then and

14. If then and

15. If then and

16. If then and

Find the value of the variable.

17. 18. 19.

20. 21. 22.

(3x � 17)�(2x � 8)�(3x � 8)�

x �(2x � 5)�75�

(48 � x)�64�

x � (5x � 48)�110�

(2x � 40)�

m�C � ? .m�� ? m�B � 45�,

m�C � ? .m�B � ? m�A � 17�,

m�C � ? .m�A � ? m�B � 78�,

m�C � ? .m�B � ? m�� 42�,

�C�B

�B�A

m�6 � ? .m�7 � 15�,

m�9 � ? .m�8 � 158�,

m�9 � ? .m�7 � 47�,

m�8 � ? .m�9 � 124�,

m�6 � ? .m�8 � 94�, 6

879

m�7 � ? .m�6 � 78�,

�5�3

�4�1

�5�2

�4�3

�2�11 2

345

�2�1

Less

on

1.6

MCRBG-0106-PA.qxd 5-2-2001 4:16 PM Page 84




LESSONNAME _________________________________________________________ DATE ___________

Lesson

1.6

1. Explain what is wrong with the following argument: Note that and are vertical angles, and and are also vertical angles. Since is a vertical angle and is a vertical angle, and vertical angles are congruent, we mayconclude that

In Exercises 2–5, tell whether the statement is true or false. If it is true,

explain why; if it is false, sketch a counterexample.

2. Given and with a common side If is a right angle, then and are complementary.

3. Given and with a common side If is a straight angle, then and are supplementary.

4. If and are a linear pair, and and are also a linear pair, then and are vertical angles.

5. If and are vertical angles, then and are a linear pair.

In Exercises 6–11, find the values of x and y in the diagram.

6. 7.

8. 9.

10. 11.

(4x � 6y)�(2x � y)�

(2x � 3y)�

(50 � y)�

(16x � 10y)�

4x�

(60 � y)�

(9y � 2x)�

(8y � 2x)�

(6x � y)�(2x � y)�

(8y � 4x)�

(x � 2y)�(2x � 12y)�

8x�(2x � 4y)�

(4x � 7y)�

50�

(x � y)�(x � y)�

�SUT�RUS�TUV�RUS

�TUV�RUS�TUV�SUT�SUT�RUS

�BCD�ACB�ACD

→CB:�BCD�ACB

�BCD�ACB�ACD

→CB:�BCD�ACB

�1 � �2.

�2�1�4�2�3�1

12

34


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