Review for Sem 1 Quiz 1
G
A
F
B
3
C
4
2
E
1
5
H
D
Name all pairs of vertical
angles
1 & 4
5 & GEC
J
G
A
F
B
3
C
4
2
E
1
5
H
D
Name all linear pairs
1 & 5
2 & AED
5 & 4
3 & AEH
1 & FEC
4 & FEC
J
G
A
F
B
3
C
4
2
E
1
5
H
J
D
Name 2 in all possible ways
AEG, AEF, BEG, BEF
GEA, FEA, GEB, FEB
G
A
F
B
3
C
4
2
E
1
5
H
D
Name 4 collinear points
C, E, H, J,
D, E, F, G
J
G
A
F
B
3
C
4
2
E
1
5
H
J
D
Name EH in all possible ways
EJ
G
A
F
B
3
C
4
2
E
1
5
H
J
D
Name CE in all possible ways
CH
CJ
G
A
F
B
3
C
4
2
E
1
5
H
D
If EC bisects AED, what
does that tell you?
3  4
J
G
A
F
B
3
C
4
2
E
1
5
H
J
D
If H is the midpoint of EJ, what
does that tell you?
EH  HJ
G
A
F
B
3
C
4
2
E
1
5
H
D
If EG bisects BEH, what
does that tell you?
2  1
J
G
A
F
B
3
C
4
2
E
1
5
H
J
D
If GF bisects CJ, what does
that tell you?
E is the midpoint of CJ and
CE  EJ
G
A
F
B
3
C
4
2
E
1
5
H
J
D
If EJ bisects DG, what does
that tell you?
E is the midpoint of DG and
DE  EG
G
A
F
B
3
C
4
2
E
1
5
H
J
D
What can you tell about 1
and 5 from the diagram?
They form a linear pair
(and are therefore supplementary)
G
A
F
B
C
3
2
1
H
Vertical 
What can you tell about 1
Thm!!
and 4 from the diagram?
4
E
5
D
They are vertical angles
(and are therefore congruent)
J
G
A
F
B
3
C
4
2
E
1
5
H
D
If m1 = 23, is 5 right,
acute or obtuse?
180 – 23 = 157, so 5 is
obtuse.
J
G
A
F
B
3
C
4
2
E
1
5
H
D
If m1 = 23, is 4 right,
acute or obtuse?
4  1, so 4 is acute
J
G
A
F
B
3
C
4
2
E
1
5
H
J
D
Given:
EC
bisects
AED
3
=
4x
+
4
3  4
3
=
4x
+
4
=
4(4)
+
4
4x + 4 = 7x – 8
4
=
7x
–
8
=
20
12 = 3x
Find m 43
=x
G
A
F
B
3
C
4
2
E
1
5
H
J
5 = 16x – 2
= 16(10) – 2
Given: 1 = 2x + 2
1 + 5 = 180
= 158
5 = 16x – 2
2x + 2 + 16x – 2 = 180
Find m 5
18x = 180
x = 10
D
2x + 40
8
Angle 8 is obtuse. Find the
restrictions on x.
90 < 2x + 40 < 180
50 < 2x < 140
25 < x < 70
9
Angle 9 is acute. Find the
restrictions on x.
0 < 5x – 35 < 90
35 < 5x < 125
7 < x < 25
Given: 10 = 8x – 6
11 = 20x + 18
Find the value of x.
11
10 + 11 = 180
8x – 6 + 20x + 18 = 180
28x + 12 = 180
28x = 168
x=6
10
Given: 12 = 10x
13 = 7x +33
Find m13.
13 = 7x + 33
12 = 13
10x = 7x + 33
= 7(11) + 33
3x = 33
= 110
x = 11
Given: O is the midpt of CW
CO = 2x – 1
OW = 3x – 10
Find the value of x.
CO = OW
2x – 1 = 3x – 10
-1 = x – 10
9=x
Given: IT bisects PG
PI = 5x + 5
IG = 8x – 55
Find the length of PI.
T
PI = 5x
PI+=5IG
+5
5x=+5(20)
5 = 8x
– 55
= 60
105= 3x
20 = x
14
Angle 14 is acute. Find the
restrictions on x.
0 < 3x + 63 < 90
-63 < 3x < 153
-21 < x < 51
Given: 15 = 14x + 9
16 = 11x +36
Find the value of x.
15 = 16
14x + 9 = 11x + 36
3x = 27
x=9
Given: AT bisects BM
AM = 3x + 2
AB = 5x – 12
Find the length of AM.
T
AM
=
AB
AM = 3x + 2
3x =
+ 3(7)
2 = 5x
–
12
+2
=14
23= 2x
7=x
Simplify.
Show your work.
6 – 4(2 • 3 – 1)  5
6 – 4(6 – 1)  5
6 – 4(5)  5
6 – 20  5
6–4
2
6x + 30
17
Angle 17 is obtuse. Find the
restrictions on x.
90 < 6x + 30 < 180
60 < 6x < 150
10 < x < 25
Simplify.
Show your work.
8 + 2(23 – 5)2
8 + 2(8 –
8 + 2(3)2
8 + 2(9)
8 + 18
26
2
5)
Given: 18 = 100x – 40
19 = 9x + 2
Find the value of x.
18
18 + 19 = 180
100x – 40 + 9x + 2 = 180
109x – 38 = 180
109x = 218
x=2
19
20
21
20 = 21
3x + 6 = 5x – 10
16 = 2x
8=x
Given: BC bisects ABD
20 = 3x + 6
21 = 5x – 10
Find the value of x.