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ompanies, Inc.
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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
Geo-SG01-02-11-846589
A C
6 in.
B23–4 in.
Geo-SG01-02-13-846589
W Y
6 cm
X
Geo-SG01-02-12-846589
X ZY
31–2 in. 3–
4 in.
Geo-SG01-02-10-846589
R T2.0 cm 2.5 cm
S
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on 1
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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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Glencoe/M
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-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
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
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–6 –4 –2 0 2 4 6 8 10
J K L M N
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on 1
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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