NAME DATE PERIOD Study Guide and Intervention

[Pages:4]NAME

DATE

1-2 Study Guide and Intervention

PERIOD

Line 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.

P

On AC , AB = BC = 3 cm. We can say that the segments are

congruent segments, or -A-B -B-C-. Slashes on the figure indicate

A

which segments are congruent.

MQ

B

C

Example 1 Find EF.

Example 2 Find x aGnedoA-SCG. 01-02-07-846589

1.2 cm

1.9 cm

E

D

F

Point D is between E and F. Calculate EF by adding ED and DF.

ED + DF = EF Betweenness of points 1.2G+eo1-.S9G=0E1-F02-0S8ub-s8ti4tu6tio5n89

3.1 = EF Simplify. Therefore, E-F- is 3.1 centimeters long.

2x + 5

A xB

2x

C

B is between A and C.

AB + BC = AC

Betweenness of points

Gexo+-S2Gx0=1-20x2-+095-8465S8u9bstitution

3x = 2x + 5

Add x + 2x.

x = 5

Simplify.

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

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Exercises

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

1. R--T

2.0 cm

R

S

2.5 cm T

2. B--C-

6 in.

A 2 3?4 in. B

C

3. X--Z

3 1?2 in.

3?4 in.

XGeo-SG01-02Y-10Z-846589

4. W--X-

6 cm

W

X

Y

Geo-SG01-02-11-846589

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

5. RS =G5exo,-SSTG0=13-0x2, -a1n2d-8R4T65=8498 7. RS = 6x, ST = 12, and RT = 72

6. RS =G2exo, S-STG=015-x0+2-143, -a8n4d6R58T9= 32 8. RS = 4x, ST = 4x, and RT = 24

Determine whether each pair of segments is congruent.

9. A-B-, -C-D-

A

11 cm

D

5 cm 5 cm

B

11 cm

C

10. X-Y-, Y-Z-

X

3x + 5

5x - 1

Geo-SG01-02-14-846589

Y

9x

Z

2

Chapter 1

12

Glencoe Geometry

Geo-SG01-02-15-846589

NAME

DATE

PERIOD

1-2 Study Guide and Intervention (continued)

Line Segments and Distance

Distance Between Two Points

Distance on a Number Line

A

B

x1

x2

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

Geo-SG01-03-01-846589-A

Distance in the Coordinate Plane Distance Formula:

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

A(x1, y1)

y B(x2, y2)

0

x

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 1-2

Example 1 find AB.

A

Use the number line to

B

Example 2 C0F1-i0n1dA-t8h9e05d1is0tance

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

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

AB = |(-4) - 2| Ge=o|-S-G60|1-03-03-846589 = 6

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

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

AB = (3)2 + (4)2

= 25 = 5

Exercises

Use the number line to find each measure.

1. BD 3. AF 5. BG 7. BE

2. DG 4. EF 6. AG 8. DE

A B C DE F

G

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

Geo-SG01-03-04-846589

Find the distance between each pair of points.

9. A(0, 0), B(6, 8) 11. M(1, -2), N(9, 13)

10. R(-2, 3), S(3, 15) 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)

Chapter 1

13

Glencoe Geometry

NAME

1-2 Skills Practice

DATE

PERIOD

Line Segments and Distance

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

1. N--Q-

2. A-C-

3. G--H-

1in.

Q

P

11?4 in. N

4.9 cm

5.2 cm

A

B

C

F 9.7 mm G

H

15 mm

GAeLoG-PERB0R1A-02F-0in3d-8t4h6e58v9alue

of

x

Geo-PR01-02-04-846589 and YZ if Y is between X and

Geo-PR01-02-05-846589 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. B--E-, C--D-

9. M--P-, N--P-

10. W--X-, W--Z-

B 2m C

3 m

3 m

E

5m D

12 yd M

12 yd

P 10 yd N

Y

9 ft

Z

5 ft

5 ft

X

W

Geo-PR01-02-06-846589 Geo-PR01-02-07-846589

Geo-PR01-02-08-846589

Use the number line to find each measure.

11. LN 13. KN

12. JL 14. MN

J

K

L

M

N

?6 ?4 ?2 0 2 4 6 8 10

Geo-SG01-03-01-846589

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)

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 1

14

Glencoe Geometry

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 1-2

NAME

1-2 Practice

DATE

PERIOD

Line Segments and Distance

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

1. P--S

18.4 cm P

4.7 cm QS

2. A--D-

2 3?8 in. A

1 1?4 in.

C

D

3. W--X-

W X 89.6 cm Y 100 cm

Geo-PR01-02-11-846589 ALGEBRA Find the value of

x

anGdeKo-LPRif0K1-i0s2b-1e2tw-8e4e6n58J9and

Geo-PR01-02-13-846589 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. T--U-, S--W-

7. A--D-, B--C-

8. G--F-, F-E-

T 2 ft S

2 ft

3 ft

U 3 ft W

A D

12.7 in. 12.9 in.

B C

G 5x F

H 6x E

Geo-PR01-02-14-846589

Geo-PR01-02-15-846589 Geo-PR01-02-16-846589

Use the number line to find each measure.

S

TU

V

W

9. VW

10. TV

?10 ?8 ?6 ?4 ?2 0 2 4 6 8

Find the distance between each pair of points.

11.

y

12.

Z

Geo-SG01-03-05-846589

y

S

O

x

M

13.

Geo-PR01-03-06-846589 L(-7, 0), Y(5, 9)

O

x

E

Geo-PR01-03-07-846589 14. U(1, 3), B(4, 6)

Chapter 1

15

Glencoe Geometry

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