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Integrated III
Segments, Lines, and Rays
Name _________________________
k
Date _______ Period ________
j
In Diagram 1, line k and j intersect at A.
Identify whether each statement is true or false.
Diagram 1
1. AB is the same as BD.F
2. AB is the same as BD.T
3. Line j contains just three points.F
4. Points C, A, and E are collinear.T
5. Points B, A, and E are collinear.F
E
B
D
A
C
j
k
k
Refer to Diagram 2 for problems #6-8.
j
Diagram 2
6. How would you read the symbol HG? segment
What does it mean?
7. Name the endpoints of HG and GH .H and G
8. How would you read the symbol FH ? ray
What does it mean?
H
G
F
Refer to Diagram 3 for problems #9-14.
Diagram 3
9. What is the coordinate of T? -3
10. What point has the coordinate of 1?E
11. Which point is the midpoint of
TE
?C
T
U
C
-3
-2
-1
12. Find TK.3
k
K
E
R
0
1
2
j
13. Find UR.4
k
14. How many real numbers are there between 1 and 2 - a limited number or an unlimited
number? how many points are there between K and E? unlimited number
j
15. Suppose LM = 4, MN = 3, and LO = 14.
L
M
N
O
a. Find NO.7
b. Is N the midpoint of LO? Explain your answer.Yes, N creates two equal parts…
(LN=7 etNO=7).
16. Suppose E is the midpoint of
.
E
O
M
G
GM
a. If GM =16, find EM. 8
b. Suppose O is the midpoint of EM . Find EO.4
k
j
In Diagram 4, G is the midpoint of TR , TI = 6, and TE = 23.
Find each of the following.
Diagram 4
17. The coordinate of G.5
T
18. The coordinate of I.-4
I
G
E
R
20
-10
19. The coordinate of E. 13
20. TG.9
21. IE. 17
22. IR. 24
In Diagram 5, Q is the midpoint of PR .
Complete the table.
(Hint: Draw a new picture for each problem.)
coordinate
of P
coordinate
of R
PR
coordinate
of Q
Diagram 5
P
Q
23.
24.
25.
26.
27.
28.
8
-4
-18
5
17
-8
12
12
-2
13
41
6
4
16
16
8
24
14
10
4
-10
9
29
-1
Draw a picture, write an equation and solve.
29. B is between A and C. AB = x, BC = x+6 and AC = 12. Find x, AB, BC.
x+x+6=12
A
B
x=3, AB=3, BC=9
C
For problems #30-33, E is the midpoint of DF . Find x.
Draw a picture, write an equation and solve.
30. DE = 5x + 3 and EF = 33.
5x+3=33
D
E
x=6
F
31. DE = 45 and EF = 5x - 10.
45=5x-10
D
E
F
R
x=11
32. DE = 3x and EF = x + 6.
3x=x+6
D
E
x=3
F
33. DE = 2x - 3 and EF = 5x - 24.
2x-3=5x-24 x=
D
E
F
E is between G and H. Find z and determine if E is the midpoint GH .
Draw a picture, write an equation and solve.
34. GE = z + 2, GH = 20, EH = 2z - 6.
z+2+2z-6=20
G
E
z=8
E is the midpoint… GE=EH=10
H
35. GH = z + 6, EH = 2z - 4, GE = z.
z+6=2z-4+z
G
E
H
z=5
E is not the midpoint…
GE=5 EH=6 GE≠EH