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