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Chapter 1 12 Glencoe Geometry

1-2 Study Guide and InterventionLine Segments and Distance

Calculate Measures On ! "# PQ , to say that point M is between points P and Q means P, Q, and M are collinear and PM + MQ = PQ.On ! "# AC , AB = BC = 3 cm. We can say that the segments are congruent segments, or

−− AB %

−−− BC . Slashes on the figure indicate

which segments are congruent.

Geo-SG01-02-07-846589

AB

C

QMP

Find EF.

Geo-SG01-02-08-846589

E1.2 cm 1.9 cm

FD

Point D is between E and F. Calculate EF by adding ED and DF. ED + DF = EF Betweenness of points

1.2 + 1.9 = EF Substitution

3.1 = EF Simplify.

Therefore, −− EF is 3.1 centimeters long.

Find x and AC.

Geo-SG01-02-09-846589

A x 2x CB

2x + 5

B is between A and C. AB + BC = AC Betweenness of points

x + 2x = 2x + 5 Substitution

3x = 2x + 5 Add x + 2x.

x = 5 Simplify.

AC = 2x + 5 = 2(5) + 5 = 15

ExercisesFind the measurement of each segment. Assume that each figure is not drawn to scale.

1. −− RT 2. −−−

BC

3. −− XZ 4. −−−

WX

ALGEBRA Find the value of x and RS if S is between R and T.

5. RS = 5x, ST = 3x, and RT = 48 6. RS = 2x, ST = 5x + 4, and RT = 32

7. RS = 6x, ST = 12, and RT = 72 8. RS = 4x, ST = 4x, and RT = 24

Determine whether each pair of segments is congruent.

9. −− AB ,

−−− CD 10. −−

XY , −− YZ

Geo-SG01-02-15-846589

X

Y Z

3x + 5 5x - 1

9x2Geo-SG01-02-14-846589

A D

CB

11 cm

11 cm

5 cm5 cm

Example 1 Example 2

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A C

6 in.

B23–4 in.

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W Y

6 cm

X

Geo-SG01-02-12-846589

X ZY

31–2 in. 3–

4 in.

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R T2.0 cm 2.5 cm

S

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Chapter 1 13 Glencoe Geometry

1-2 Study Guide and Intervention (continued)

Line Segments and DistanceDistance Between Two Points

Distance on a Number Line Distance in the Coordinate Plane

Geo-SG01-03-01-846589-A

A B

x1 x2

AB = |x1 - x2| or |x2 - x1|

Distance Formula:

C01-01A-890510

y

x

B(x2, y2)

A(x1, y1)

d = √ """"""""" (x2 - x1)2 + (y2 - y1)

2

Use the number line to find AB.

AB = |(-4) - 2| = |- 6| = 6

Geo-SG01-03-03-846589

-5 -4 -3 -2 -1 0 1 2 3

A B

Find the distance between A(-2, -1) and B(1, 3).Distance Formula

d = √ """"""""" (x2 - x1)2 + ( y2 - y1)

2

AB = √ """""""""" (1 - (-2))2+ (3 - (-1))2

AB = √ """" (3)2 + (4)2

= √ "" 25 = 5

ExercisesUse the number line to find each measure.

1. BD 2. DG

3. AF 4. EF

5. BG 6. AG

7. BE 8. DE

Find the distance between each pair of points.

9. A(0, 0), B(6, 8) 10. R(-2, 3), S(3, 15)

11. M(1, -2), N(9, 13) 12. E(-12, 2), F(-9, 6)

13. X(0, 0), Y(15, 20) 14. O(-12, 0), P(-8, 3)

15. C(11, -12), D(6, 2) 16. K(-2, 10), L(-4, 3)

Geo-SG01-03-04-846589

-10 -8 -6 -4 -2 0 2 4 6 8

A B C D E F G

Example 1 Example 2

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Chapter 1 14 Glencoe Geometry

Skills PracticeLine Segments and Distance

Find the measurement of each segment. Assume that each figure is not drawn to scale.

1. −−− NQ 2. −−

AC 3. −−− GH

ALGEBRA Find the value of x and YZ if Y is between X and Z.

4. XY = 5x, YZ = x, and XY = 25 5. XY = 12, YZ = 2x, and XZ = 28

6. XY = 4x, YZ = 3x, and XZ = 42 7. XY = 2x + 1, YZ = 6x, and XZ = 81

Determine whether each pair of segments is congruent.

8. −−− BE ,

−−− CD 9. −−−

MP , −−− NP 10. −−−

WX , −−− WZ

Use the number line to find each measure.

11. LN 12. JL

13. KN 14. MN

Find the distance between each pair of points.

15. K(2, 3), F(4, 4) 16. C(-3, -1), Q(-2, 3)

17. Y(2, 0), P(2, 6) 18. W(-2, 2), R(5, 2)

Geo-PR01-02-06-846589

E D

CB

5 m

2 m

3 m 3 m

Geo-PR01-02-05-846589

F 9.7 mm HG

15 mm

Geo-PR01-02-04-846589

A4.9 cm 5.2 cm

CB

Geo-PR01-02-03-846589

Q1in. 11–

4 in.

NP

1-2

Geo-PR01-02-07-846589

N

P

M 10 yd

12 yd

12 yd

Geo-PR01-02-08-846589

Y Z

WX

9 ft

5 ft 5 ft

Geo-SG01-03-01-846589

–6 –4 –2 0 2 4 6 8 10

J K L M N

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Chapter 1 15 Glencoe Geometry

PracticeLine Segments and Distance

Find the measurement of each segment. Figures are not drawn to scale.

1. −− PS 2. −−−

AD 3. −−− WX

ALGEBRA Find the value of x and KL if K is between J and L.

4. JK = 6x, KL = 3x, and JL = 27 5. JK = 2x, KL = x + 2, and JL = 5x - 10

Determine whether each pair of segments is congruent.

6. −−− TU ,

−−− SW 7. −−−

AD , −−−

BC 8. −−− GF , −−

FE

Use the number line to find each measure.

9. VW 10. TV

Find the distance between each pair of points.

11.

Geo-PR01-03-06-846589

x

y

OM

Z 12.

Geo-PR01-03-07-846589

x

y

O

E

S

13. L(-7, 0), Y(5, 9) 14. U(1, 3), B(4, 6)

Geo-PR01-02-16-846589

G H

EF

5x

6x

Geo-PR01-02-15-846589

D C

BA

12.9 in.

12.7 in.

Geo-PR01-02-14-846589

W

T S

U

2 ft

2 ft

3 ft

3 ft

Geo-PR01-02-13-846589

W 89.6 cm YX

100 cm

Geo-PR01-02-12-846589

A

11–4 in.23–

8 in.

DC

Geo-PR01-02-11-846589

P4.7 cm18.4 cm

SQ

1-2

Geo-SG01-03-05-846589

–6 –4–10 –8 –2 0 2 4 6 8

S T U V W