Geometry Accelerated
Chapter 6 Practice Quiz
Name:__________________
12/8/12
1st/5th period
A.M.D.G.
1. If I have a regular dodecagon, find each of the following:
a. The total measure of all of the interior angles.
b. The measure of each interior angle.
c. The total measure of all of the exterior angles.
d. The measure of each exterior angle.
a) (12 – 2)180° = 1800°
b) 1800/12 = 150°
c) 360° (all polygons have a total of 360° for exterior angles)
d) 360/12 = 30°
2. Given the figure below, solve for x.
Y
A
74°
X
62°
x2 +10x + 60°
108°
B
8x + 2°
R
The figure is a pentagon, so the interior angles total 540°
62° + 108° + 8x + 2° + 74° + x2 +10x + 60° = 540°
x2 +18x – 234° = 0
x = 8.748° or -26.748° (using the quadratic formula)
Since the negative number gives a negative angle at R, x = 8.748°
3. Solve for x and y in the figures below. (5 points)
a)
b)
7m
7m
x
22 cm
cm
x2 – 3x
10 m
14 cm
a) Since the figure is a trapezoid:
14  22
 x 2  3x
2
0  x 2  3x  18
0   x  6  x  3
x  6 or  3
10 m
8m
b) This is a kite, so diagonals are perpendicular:
Pythagorean Theorem:
x 2  82  102
x 2  36
x6
4. A regular polygon has interior angles of 157.5°. Find the number of sides that the regular
polygon must have.
 n  2 180
 157.5
n
 n  2 180  157.5 n
180n  360  157.5n
22.5n  360
n  16
Therefore, it has 16 sides.
5. Find the area of each figure below. (10 points)
a) 101.5 cm2
c) 85.5 m2
19 cm
7 cm
d1 = 9 m
d2 = 19 m
10 cm
b) 71.5 cm2
d) 391 cm2
13 cm
17 cm
11 in
23 cm
6. Find the value of x, y, and z in the figures below.
a) ABCD is a trapezoid with
b) ABCD is a rhombus
area of 127 cm2
AP  5 y  1 , CP  2 y  12 ,
BP  2 z 1, PD  z  5
A
4x  7
D
D
A
12 cm
B
P
7x  3
1
 4 x  7  7 x  312   127
2
6 11x  10   127
66 x  60  127
66 x  187
x
C
B
C
5 y  1  2 y  12
3 y  11
11
y
3
2z 1  z  5
z6
187
cm
66
7. Identify each of the following quadrilaterals as specifically as possible using the
information given on the diagram.
a.
c.
Rectangle
Trapezoid
b.
d.
Parallelogram
Trapezoi
8. Use a coordinate proof to prove the quadrilateral below is a kite.
y
D
(0,a)
(-b,0)
(b,0)
P
x
X
R
(0,-c)
Use Distance Formula on each side to prove adjacent sides are equal.
RP 
 b  0    0   c  
2
RP  b 2  c 2
RX 
2
PD 
 b  0    0  a 
2
PD  b 2  a 2
 b  0    0   c  
2
RX  b 2  c 2
Therefore it is a kite.
2
XD 
b  0   0  a 
2
XD  b 2  a 2
2
2
9. Prove the quadrilateral below is a parallelogram.
y
D
(-b,0)
(b,a)
X
P
x
(b,0)
R
(-b,-a)
Prove opposite sides are parallel by showing they have the same slopes:
b  b
0a
0
mRP 
mRP
bb
a0
0
mDX 
mDX
bb
a0
2b

a
mPD 
mPD
bb
0a
2b

a
mRX 
mRX
Since opposite sides are parallel, the figure is a parallelogram.