ac1.3hmorepracticeproblems
DESCRIPTION
More practice problems for geometry number line distance. This is for high school students.TRANSCRIPT
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Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
1.3 Segments, Rays, and DistanceWE Page 15
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1.3 Segments, Rays, and DistanceWE Page 15
The numbers given are coordinates of 2 points on a number line. Find the distance between the points.
1. - 6 and 9 2. - 3 and - 17
3. - 1.2 and - 5.7 4. - 2.5 and 4.6
9 ( 6) 15 17 ( 3)
17 3 14
1.2 ( 5.7)
1.2 5.7 4.5 4.6 ( 2.5)
4.6 2.5 7.1
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In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
5. H
KM
T
L
LM MH
HL KT�������������� �
HL
True. It goes through midpoint.
True. The order of the letters doesn’t matter.
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In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
5.
6. KM must = MT
H
KM
T
L
LM MH
HL KT�������������� �
HL
False. KM < MT
True. The order of the letters doesn’t matter.
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In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
5.
6. KM must = MT
7. bisects
8. is a bisector of
H
KM
T
L
LM MH
HL KT�������������� �
HL
MT LH
LHKT�������������� �
True. It goes through midpoint.
True. It goes through midpoint.
False. KM < MT
True. The order of the letters doesn’t matter.
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9. and are opposite rays.
10. and are opposite rays.
11. is the same as
12. is the same as
H
KM
T
L
MT��������������
TM��������������
False. They do not have the same endpoint.
MT��������������
MK��������������
LH�������������� �
HL
KT��������������
KM��������������
True.
False. One’s a line & the others a segment.
True. They have same starting point and direction.
In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
HL KT�������������� �
HL
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13. is the same as
14. is the same as
15. HM + ML = HL
H
KM
T
L
In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
HL KT�������������� �
HL
KT�������������� �
KM�������������� �
KT�������������� �
KM
True. Same line but different points.
False. One’s a line & the others a segment.
True. Segment Add. Postulate.
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13. is the same as
14. is the same as
15. HM + ML = HL
16. TM + MH = TH
H
KM
T
L
In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
HL KT�������������� �
HL
KT�������������� �
KM�������������� �
KT�������������� �
KM
True. Same line but different points.
False. One’s a line & the others a segment.
True. Segment Add. Postulate.
False. Shortest distance between 2 points is a straight line.
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17. T is between H and M.
18. M is between K and T.
H
KM
T
L
In the diagram, and intersect at the midpoint of . Classify each statement as true of false. State why the statement is false.
HL KT�������������� �
HL
False. T is not on segment HM.
True. M is on segment KT.
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Name each of the following.
19. The point on whose distance from D is 2.
DB C GFEA
- 3 - 2 - 1 0 1 2 3
DA��������������
B
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Name each of the following.
19. The point on whose distance from D is 2.
20. The point on whose distance from D is 2.
DB C GFEA
- 3 - 2 - 1 0 1 2 3
DA��������������
DG��������������
B
F
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Name each of the following.
21. Two points whose distance from E is 2.
DB C GFEA
- 3 - 2 - 1 0 1 2 3
C and G
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Name each of the following.
21. Two points whose distance from E is 2.
22. The ray opposite to
DB C GFEA
- 3 - 2 - 1 0 1 2 3
BE��������������
C and G
BA��������������
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Name each of the following.
23. The midpoint of
DB C GFEA
- 3 - 2 - 1 0 1 2 3
BF
D seen visually. orAverage the coordinates.
2 20
2
Note that the name of the midpoint is a letter while the coordinate is a number.
D
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Name each of the following.
24. The coordinate of the midpoint of
DB C GFEA
- 3 - 2 - 1 0 1 2 3
-1 seen visually. or
Average the coordinates.
2 01
2
BD
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Name each of the following.
25. The coordinate of the midpoint of
DB C GFEA
- 3 - 2 - 1 0 1 2 3
AE
-1
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Name each of the following.
25. The coordinate of the midpoint of
26. A segment congruent to
DB C GFEA
- 3 - 2 - 1 0 1 2 3
AE
BGAF
-1
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In Exercises 27-30 draw and so that the
conditions are satisfied.
27. Segments CD and RS intersect, but neither segment bisects to other.
28. Segment CD and RS bisect each other.
R
SC
D OR R S
C
D
OR
R
S
C
D
R
S
C
D
CD RS
There are an infinite possibilities.
There are an infinite possibilities.
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29. bisects but doesn’t bisect
OR
R S
C
D
R SC
D
In Exercises 27-30 draw and so that the
conditions are satisfied.CD RS
CDCD
RSRS
There are an infinite possibilities.
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30. and do not intersect.
ORC
R
DS
R
DC
S
In Exercises 27-30 draw and so that the
conditions are satisfied.CD RS
CD RSBut and do intersect. CD��������������
RS�������������� There are an
infinite possibilities.
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31. In the diagram, , S is midpoint of .
QR = 4 and ST = 5. Complete.
PR RT RT
P Q R S TLabel DiagramFirst !! 4 5 5
1010
6
a] RS = _____ b] RT = _____
c] PR = _____ d] PQ = _____
5 10
10 6Note that once the diagram was labeled, everything was easier.
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32. In the diagram, X is the midpoint of
VW = 5, and VY = 20. Find the coordinates of W, X, & Y.
VZ
V W X Y Z
5
20
34- 12 22
17 17
Label Diagram
22 ( 12) 34
X = -12+17 = 5W = -12+ 5 = -7
Y = -12+20 = 8
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33. DE = 5x + 3 , EF = 33
E is the midpoint of . Find the value of x.
F
D
HG E
DF
5x + 3 = 33
5x = 30
x = 6
33
5x + 3
Label the diagram first
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34. DE = 45 , EF = 5x - 10
E is the midpoint of . Find the value of x.
F
D
HG E
DF
45 = 5x - 10
55 = 5x
11 = x
5x - 10
DE = 45
Label the diagram first
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35. DE = 3x , EF = x + 6
E is the midpoint of . Find the value of x.
F
D
HG E
DF
3x = x + 6
2x = 6
X = 3
EF = x + 6
DE = 3x
Label the diagram first
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36. DE = 2x - 3 , EF = 5x - 24
E is the midpoint of . Find the value of x.
F
D
HG E
DF
2x – 3 = 5x - 24
-3x -3 = -24
- 3x = - 21
x = 7
Label the diagram firstCC5x - 24
2x – 3
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37. GE = y , EH = y – 1 , GH = 11
Find the value of y.
F
D
HG E
y + y - 1 = 11
2y - 1 = 11
2y = 12x = 6
Segment Addition Postulate
Sum of the parts = the whole.
y y – 1Label the diagram first
GH = 11
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38. GE = 3y , EH = 24 , GH = 7y - 4
Find the value of y.
F
D
HG E
3y + 24 = 7y - 4
24 = 4y - 4
28 = 4y
7 = y
Segment Addition Postulate
Sum of the parts = the whole.
3y 24Label the diagram first
GH = 7y - 4
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39. GE = z + 2 , EH = 2z - 6 , GH = 20
Find the value of z. Then find GE and EH and state whether E is the midpoint.
F
D
HG E
z + 2 + 2z - 6 = 20
3z - 4 = 20
3z = 24
z = 8
Segment Addition Postulate
Sum of the parts = the whole.
GE = z + 2 = 10
EH = 2z – 6 = 10
E is a midpoint.
z + 2 2z - 6Label the diagram first
GH = 20
Not done yet. Find segments.
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40. GE = z , EH = 2z - 4 , GH = z + 6
Find the value of z. Then find GE and EH and state whether E is the midpoint.
F
D
HG E
z + 2z - 4 = z + 63z - 4 = z + 6
2z - 4 = 6
2z = 10
Segment Addition Postulate
Sum of the parts = the whole.
GE = z = 5
EH = 2z – 4 = 6
E is not a midpoint.
z = 5
z 2z - 4Label the diagram first
GH = z + 6
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41.
Name the graph of the given equation or inequality.
2 2x NH M ZYTG
- 4 - 2 0 2 4 6 8
42. 0x
HN
MH or MG����������������������������
43. 4x
4 4x GT
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44.
Name the graph of the given equation or inequality.
0x NH M ZYTG
- 4 - 2 0 2 4 6 8
45. 0x
GH�������������� �
The whole line.
Point M
The absolute value of negative numbers are greater than 0; the absolute value of 0 = 0 ; and the absolute value of positive numbers are greater than zero.
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46a.
Draw the diagram and illustrate your answer.
46b.
On , how many points are there whose distance
from point A is 3 cm.
AB��������������
3 cm
A
B
1
On , how many points are there whose distance
from point A is 3 cm.
AB�������������� �
3 cm 3 cm
A
2
B
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C’est fini.
Good day and good luck.