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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