Ac1.3hMorePracticeProblems
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Transcript of Ac1.3hMorePracticeProblems
Millau BridgeSir Norman Foster
Point, Lines, Planes, Angles
FallingwatersFrank Lloyd Wright
Millenium ParkFrank Lloyd Wright
1.3 Segments, Rays, and DistanceWE Page 15
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
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.
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.
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.
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
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.
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.
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.
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
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
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
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��������������
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
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
Name each of the following.
25. The coordinate of the midpoint of
DB C GFEA
- 3 - 2 - 1 0 1 2 3
AE
-1
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
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.
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.
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.
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.
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
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
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
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
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
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
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
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.
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
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
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.
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
C’est fini.
Good day and good luck.