Geometry A
Review for Quiz 2
Name ____________________
Date ________________
1. What can you assume (and not assume) from looking at a diagram?
See blue box on p. 19
2. What is an acute angle? Obtuse?
Between 0˚ and 90˚; between 90˚ and 180˚
3.
1
2
 What can you conclude about angles 1 and 2? They are a linear pair,
and therefore supplementary.
 If m  1 = (x2 + x + 100)°
m  2 = (4x + 56) °
Find the measure of  1
x2 + x + 100 + 4x + 56 = 180
x2 + 5x – 24 = 0
(x + 8)(x – 3) = 0
x = -8 x = 3
m<1 = (-8)2 + (-8) + 100 = 156˚
m<1 = (3)2 +(3) + 100 = 112˚
4. Draw line p that intersects plane H at point G; points G, A, and B are
collinear and all contained in plane H.
p
A
5. Solve
𝑥=
7x2 + 2x – 1 = 11x2 – 3x – 5
0 = 4x2 – 5x – 4
5±√25−4(4)(−4)
2(4)
=
5±√−39
8
no solution!
H
G
B
6. Solve:
10x - 8 = 6x2 + 3x – 11
0 = 6x2 – 7x – 3
0 = (2x – 3)(3x + 1)
x = 3/2 x = -1/3
7. Solve:
33x 2  10 x  22  8 x 2  10 x  1
25x2 – 20x – 21 = 0
0 = (5x – 7)(5x + 3)
x = 7/5 x = -3/5
8. Ray CD bisects segment EF at point J. EF = 5x + 1 and EJ = 3x – 1.
Draw a diagram to accurately represent this situation, and find the length of
segment JF
D
2(3x – 1) = 5x + 1
E
J
F
6x – 2 = 5x + 1
x=3
3x – 1
C
JF = 3x – 1
= 3(3) – 1
5x + 1
=8
9. Ray CD bisects  BCW. m  DCW = 8x – 1 and m  DCB = 12x – 29.
Draw a diagram to accurately represent this situation, and find the measure
of  BCW.
12x – 29 = 8x – 1
(12x - 29)°
B
4x = 28
D
x=7
(8x – 1)°
C
W
<BCW = 2(8x – 1)
= 2(8•7 – 1)
= 110˚
10. The sum of an angle and twice its supplement is 144 more than 3
times the angles complement. What is the angles complement?
x + 2(180 – x) = 144 + 3(90 – x)
x + 360 – 2x = 144 + 270 – 3x
-x + 360 = -3x + 414
2x = 54
x = 27
complement = 90 – 27
= 63˚
Graph each of the following:
1
4
11. y  3  x  2   3
2
12. y  x 2  x  3
-b/2a = -1/(1/2) = -2
(-2,
y = ¼ (4) + -2 – 3 = -4
13. The measure of an obtuse angle is (2x + 50)°. What are the
restrictions on x?
Skip (not on quiz!)
14. Draw a pair of adjacent angles.
Draw a pair of vertical angles.
15. What is the difference between:
a) a Postulate and a theorem? A thm is proven
b) a midpoint and a segment bisector? Midpoint is a POINT;
segment bisector is a segment, ray, line, plane, etc that goes thru the midpt
c) complementary and supplementary angles? Complementary = 90;
Supplementary = 180
d) a line, a segment and a ray? A segment has 2 endpoints; a ray
has one and a line has no endpoints—it is infinite in both directions.