Review for Quiz
Aims 1-4
Common Core Geometry
1. For each term below, write a brief definition, and draw a diagram for each.
Diagram
90-x
x
180-x
x
angles formed by two pairs of
1 2 3
4
b
measures of the two interior opposite
a
c
Linear Pair of
common sides form a line
b.
a.
c.
1050
1420
1420
550
1200
1050
a)
b)
(4x - 3)
x = 12
x = 17
2 = 4y - 20, solve for y.
2x + 56 = 5x + 20
4y - 20 = 100
x = 12
y = 30
m 3 = 80
m 2 = 100
5. Solve for the variables, using an auxiliary line.
b)
34
34
72
22 x
82 22
60
120
72
x = 220
0
e)
d)
c)
130
116
125
130
50
110
60
2x + 10
134
125 55
134
55
125
70
x
2x+10+60=180
x = 55
x = 22
x = 70, y = 125
6. In the diagram below, find the measure of
BFD.
28
148 32
82
142
38
60
E
D
7. In the triangle below, ABC is an isosceles triangle
with AB = BC, and BCD is an isosceles triangle with
BC = CD. If ABC = 44º, find the measure of BDC.
44 82
68
34
68
D
8. What is the measure of an exterior angle of an equilateral triangle?
9. In ΔABC,
C. If AB = x2 + 8x, BC = 3x + 5 and AC = 20, find the
perimeter ΔABC.
B
x2 + 8x = 20
x2 + 8x - 20 = 0
2
x
(x + 10)(x - 2) = 0
A
10. In the diagram below,
BCA = 8x – 15,
x = -10 / x = 2
DBC = 2x + 12 and <BDC = 4x + 9.
Find m BCD.
8x-15 = 2x + 12 + 4x + 9
2x = 36
x = 18
2x+12
129
8x-15
4x+9
11. In isosceles triangle ABC, m A = m C. If AB = 2x – 4, BC = x + 8, and
AC = 3x – 13, find the length of each side of the triangle.
B
2x - 4 = x + 8
x = 12
2x-4
A
x+8
3x-13 C
12. In the diagram, m ABC = 8x + 4, m BAC = x2 + 4x, and m ACD = 9x + 58.
Find m ACB.
9x + 58 = x + 4x + 8x + 4
+4x
2
+ 3x - 54 = 0
(x + 9)(x - 6) = 0
0
9x+58
8x+4
D
x = -9/ x = 6
0
13. In the below figure: ABC is an equilateral triangle. If m DBC = 25˚, find the
measure of
BDC.
250
0
600
0
D