Download X - Barrington 220

Geometry B
Name
Hour
Second Semester Final Review 2011
Determine whether each statement is always, sometimes, or,never true.
N
1.
Diagonals of a trapezoid are perpendicular.
2.
Adjacent sides of a rectangle are congruent. S
3
Opposite angles of a trapezoid are congruent. ~
4.
Adjacent angles of a rhombus are supplementary and congruent.
5.
Diagonals of a square are perpendicular.
6.
A trapezoid is a parallelogram.
7.
Both pairs of opposite angles of a parallelogram are congruent.
8.
The diagonals of a parallelogram are congruent.
9
Diagonals of a trapezoid are congruent.
10.
Opposite sides of a rectangle are congruent.
II.
Base angles of an isosceles trapezoid are congruent.
12.
Opposite angles of a rhombus are supplementary and congruent.
13.
Diagonals of a square are congruent.
14.
A square is a rhombus.
IS.
All angles of a parallelogram are congruent.
16.
The diagonals of a parallelogram are perpendicular.
17.
The diagonals of a rectangle are perpendicular. S
18.
Consecutive sides of a rhombus are congruent.
A
19.
A diagonal of a square bisects opposite angles.
A
20.
If a quadrilateral has two adjacent sides congruent, then it is a parallelogram.
21.
Consecutive angles in a parallelogram are complementary.
S
A
N
A
5
S
A
AS
A
AS
n If ABCD is a parallelogram, then A C == BD.
5
N
S
A
23
A regular polygon has all of its sides congruent.
24.
If a quadrilateral has four congruent sides, then it is a regular polygon.
25.
If the area of a circle is 1OJT , then the circumference is 20JT.
26.
A regular polygon has all of its angles congruent.
27.
If an octagon is convex, then it must be regular.
28.
If the circumference of a circle is 16JT, then the area is 24JT
29.
If a polygon is regular, then it is concave.
30.
A polygon is equiangular if it is regular.
31.
Square ABCD is a regular polygon.
32.
Octagon MNOPQRST is a regular polygon.
IV
A-
A
5
N
A
5
.!/
5
5
Determine if each statement is true or false.
T 33.
F 34.
A quadrilateral is a parallelogram if it has one pair of opposite sides congruent.
~
A quadrilateral is a parallelogram if it has one pair of opposite sides parallel and the other pair of opposite
35.
A quadrilateral is a parallelogram if it has both pairs of opposite angles congruent.
sides congruent.
T
36.
All isosceles right triangles are similar.
37.
All congruent quadrilaterals are similar.
38.
All squares are similar.
oF
-r
39.
All parallelograms are similar.
I
40.
All congruent rhombuses are similar.
41.
No scalene triangles are similar.
F"
42.
All similar isosceles triangles are congruent.
43.
If a polygon is equilateral, then it is regular.
44.
A regular polygon is equiangular.
T
T
r
,..
F 45.
An equiangular quadrilateral is a regular quadrilateral.
,.
46.
A square is both an equilateral and an equiangular quadrilateral.
.,-
47.
There exists a polygon such that the sum of the measures of the interior angles is 180.
t:
r
48
There exists a regular polygon such that the measure of each exterior angle is 25.
49.
The lengths of the sides of a right triangle can be 5, 6, and 7 inches.
,...
50.
The area of a parallelogram is the product of a base and the corresponding altitude.
51.
In a circle, congruent chords have congruent major arcs.
52.
A diameter of a circle is a chord of the circle.
f"
53.
If an angle is inscribed in a semi-circle, then the angle is an acute angle.
f'
54.
If two angles intercept the same arc of a ci~cle, then the two angles are congruent.
,-
55.
A line perpendicular to a radius of a circle might be tangent to the circle.
'T
T
MULTIPLE CHOICE
RIGHT TRIANGLES
56.
Given the diagram as marked below, which proportion is true?
c
AD
DB
AC
BC
BA
b. --BC
AD =AC
AC
AB
AC
d. --CD
a.-=-
o
\:J
57
BC
AD
~
CD
A
0
BC
Using the diagram for #56, CB is the geometric mean between:
a. AC and BC
GAB
and BD
c. AD and BC
d. AD and DB
B
58.
t1.ABC is a right triangle with LC being the right angle. If AB = 15 in. and BC = 8 in., then calculate AC.
:~
(Your answer must be in simplified square root form.)
(0Jl6l
59.
in.
7m in.
615
c.
in.
C CO
d. 17 in.
B
Which of the following is a Pythagorean triple?
b. 2,3,4
(y3,4,5
60.
b.
c. 7,23,25
d. 4,16,20
The length of each side of an equilateral triangle is 32 inches. Determine the length of an altitude to a side.
a. 8 inches
b. 8/3
inches
&.1..
G)16.J3 inches
c. 16 inches
ltD
61.
The length of each side of a square is 416 inches long. Determine the length of either diagonal.
X-::.4~
a. 416 in.
8/3 in.
c. 1212 in.
d. 24 in. ~f -:..)(.)2.
G)
62.
cm.
b.
=
4V1'L
3 cm., determine the
1212
3r~
lip
63.
If the length of the diagonal of a square is
a. 9 in.
64.
018
4.512
B
cm.
c
..:'_
3~
D
d. 36 in.
b.
J34
cm.
c.6cm.
@15cm.
c. 6 inches
~4inches
d. "194 inches
b
d
x
~
~ 1.. of. 11-::.
Which 30° - 60° - 90° triangle is labeled correctly?
a
0
A rectangle with width 7 inches is inscribed in a circle with diameter 25 inches. What is the length of the
other side of the rectangle?
a. 12 inches
66.
'."
inches long, then calculate the perimeter of the square.
c. 27 in.
in.
3
!»
::J _ __10
The adjacent sides of a rectangle are 9 and 12 centimeters long. How long is each diagonal?
a.4cm.
65.
@6+312
cm.
~
4~~~
'.L".~"~
cm.
~5° _
c. 9+3/3
~
x
~
(,
q\ffpn
Given the diagram as marked below. If AC
perimeter of t1. A CB .
a. 12/3
~~
~.
2S '2,..
Which 45° - 45° - 90° triangle is labeled correctly?
67.
a
b
~2'
'
'U
~,
'u
XJ2
x
x
AREA
68.
If the length of the side of a square is doubled, then:
G) the perimeter is doubled and the area is multiplied by 4
b. the perimeter is multiplied by 4 and the area is doubled
c. the perimeter and area are both doubled
d. the perimeter and area are each multiplied by 4
69.
a.
2413
units
c. 64 units
70.
@9613
2
units
d. 72 units
2
C
If C = 7rd, then - =?
d
(Answer should be exact.)
22
d. 3.14
7
A circle is inscribed in a square whose side is 16 inches. The circumference of the circle is:
o
16 7r inches
c. 87r inches
d. 4 7r inches
What is the length of a side of a square whose area is 121 square centimeters?
b. 25 cm.
a. 60.5 cm.
73
2
c.
a. 64 7r inches
72.
-:.i(1f.n) (4 B)
-= q~~
2
a. 27r
71.
A:!{A;P
The area of a regular hexagon inscribed in a circle of radius 8 units is:
@lcm.
d. 1,000 cm.
In circle Q below, if mLAQB = 45° and QB = 8 inches, then calculate the area of sector QAB.
A
a. 27r in 2
~7r
2
in
Q
C.
47r in 2
d. 37r in 2
1/5"
8
B
CIRCLES
74.
In circle 0, mAD = 44°. Determine mLABD.
...... " A
c. 88°
75.
In circle 0, mBC = 160°. Determine mLDBC.
,t.O"
H?O
-t~o
c. 20°
c
--=-10
~t 'l-O')
"2~L::.
76.
If circle 0 has a radius of 6 inches and chord AB is 3 inches from 0, how long is AB?
a.
313
(9 613 inches
inches
.. ~.SSA
3Ji \-~J3
~~ ~
..
B.~
::. (,~
c. 5 inches
n
,0.
_.
20
--:z:o
d. 80°
D
B'
~ 'Z. .f- '31:. (p 'Z.
(,
)( "l..
0
d. 10 inches
X~
2.~
VZf-:JCJJ3
':.. ~
DA and EB are diameters of circle O. EB II DC and mLDOE = 60°. Determi~e m~A
a. 15°
':.
b. 20°
A
c. 30°
+---->
78.
If DC
is tangent to circle 0 at point D, then which of the following is a right triangle?
a. /)'CAD
b. /)'AOD
c. /).COE
79.
A
In circle 0, mAE = 80°, mBfj = 144°, and
mOC = 62°.
c
Determine mLBPD.
p
LP ~
\.('44'-1-4)
-=- \'l1tJ)~2>S"
(,'2,.'
m~~ 3bO-(90~1~~t~~)
=-=1-4.
80.
Given AP and BP are tangent segments to~j~cle O. If mLAOP = 20
0
a. 500
,
then mLAPB =?
b. 800
c. 1000
0
lO
@140
p
X 1..
140.
81.
If the diameter of a circle measures 34 cm. and a chord meawres 16cm., then calculate the distance between
the chord and the center of the circle.
thottL
\'D
a. 30 cm
d. 8 cm
c. 17 cm
Short Answer
Solve each proportion using cross products.
82.
x =~
16
224
~
~ill
2'1'f't :. 2.4~~
Q=--"- ~
83
27
216
'"
IOIf)
~7-x -:.2gl)~
Determine whether each pair of triangles is similar. If they are similar, give a reason.
86.
88. Use the figure at the right to determine QR ifMN = 16, NO = 12, and PQ = 14.
I~
..---'
14
Il1
-- X
x+6
85.--x
7
4
=-
89. Complete each statement.
AB
---
AG
BC -~~
AD
AE
8t>
GE
---
90. Find the geometric mean between 9 and 25 ..
---
'f=
AC
---
BC
GF
GF
BC
CD -
Fe...
)(
q
X :. ZI5
- -
Use figure to solve each problem.
l
91. Find KM if JM = 3 and LM = 12.
92. Find JK if JL = 45 and LM = 40.
K
\'2.
3~ )(
[X':fo]
~
-S -- -45 [X:2ISJ
)(
>(
,~~o-=
?O,?
Z~C3
~
~x
93. Find JM and LM if JK = 15 and JL = 30.
900 """"1 c:..
Lm :- 2.0-+-.5"
r. J
.;;7: 2-'2.. ~
)( -:.-l.~.;,
For questions 94 and 95, assume MBC is a right triangle with the right angle at A.
..)1fY\ • • I -
94. Find BC if AB ~ 8 and AC ~ 15.
95. Find AB if AC ~ 30 and BC ~ 34.
@
@
Determine whether a triangle with sides having the given measures is a right triangle.
96. 7,10, 14
97.
0.9, 1.2, 1.5
98.
1.5, 3, 2
99. In a right triangle, the measures of the legs are x and 2x+2, and the measure of the hypotenuse is 2x+3. Find
the measure of the hypotenuse.
'Z.
1.
rr:=>"
.,
, J
(~), t(2:t tt)
3;
~~
~alueofx.
X 1- .•. Lt)( 1
~
2Xt'2..
100.
101.
102.
~(ll(~~)
t-4 : L/ xz. ~ 'l.xfGl
y. 1.-4x-5 =- 0
(?( -5)C';t 1-1) ~
8)(
0
G-t?J
')( :.. - I
12
O1(fS) + 3
::ffi
x
103.
29
UJS
"-
t.Gf
5 z. -7
X~41.1
Find the value of x.
106.
105.
x
5in
18 m
14 m
X
5(P"=
;5
x
X -;- rl..4 crt-'
107.
108.
SKIP
SKIP
State the trigonometric ratio that corresponds to each value and angle given.
SOH- c:.AH-TOA
:~
N
15
15
109.
112.
115.
-'LL
8'
110.
I~
17'
15
8
-'LM~
15 '
8
-'LM
113.
~
]j;LL
S',n
S i()
-'LM
114.
8
-'LL
17 '
Cos
US
Circle C has center at (2,3). The circle contains points A(2, 8), B(2, -2), M(-3, 3), and N(7, 3). Find the
diameter and the radius of the circle .
---------.
-=
~
"2)
1l~-a)'
J
-z.
116.
15
17'
Ill.
E;}
.l>i5~
0- Li)\-
0
"
0-'2..5"-- -=- 5 rdd;\J~
to .,o.d i liS
1+
• 2. -=- '0
Write an equation for a circle with center at (-1, -3) and a radius of 6 units.
(X _\.'))'2..
(~-r f) '" r (j +;)' -=- ~~
dAvlJ.-e-
~
C(; ~
t- <..~
(h,lL)
- 'tC-') ••.•~ V""2-
":~y
Y ':. r~;tI~
For 117 and 118 use circle T. If m<QTP = 80, m<PTU = 70, m<UTS = 30, PRand
find each measure.
117.
mPQ
QS are diameters,
p
118.
mLRTQ
u
R
119.
Suppose a chord of a circle is 48 meters long and is 10 meters from the center of the circle. Find the length
of the radius.
120.
I D'Z-
l- 1...-4"2..
=-
:. ~
2-& V"'--"
Suppose the diameter of a circle is 30 inches long and a chord is 8 inches long. Find the distance from the
15 Z, _
center of the circle to the chord.
J wq = ~
42-:..
For 121 and 122, use quadrilateral DEFG inscribed in the circle. If m<GFE
and m<EDG = 2x+20, find each measure.
?,."I..
4J)
'2.~"
121.
mLGFE
122.
mLDEF
o
G
~lL\Q) -\l. ~ (O~.
I~O-r2.
~J\l:
~y...•rt,
=
IV. 5
jY'\J
2x, and m<FGD
=
2x-12,
Find the value of x. Assume center C. Assume segments that appear to be tangent are tangent.
123.
124.
125.
1st i( IlkJ-X))
x
3D::' '00 -)(
126.
127.
EOJ
128.
210
)( -:"-J'ilO- ISO ~~
J
0z.:; 5 ( :t-f-S)
100 -=. 5)(.,. 2.5
129.
2
7-'5 ~5x
~IS1
8
3
3)(
130. The sum ofthe
:.11,
rCas::f1
[l(
(n-'2-) I'i/O
polygon contain?
. es does the
e interior angles of a convex polygon is 1620° .
::: I "'1.-0
~
V1-L..~'1
~
131. find. the sum of the measures of the exterior angles of a convex 17-gon.
C¥.j
*"J
(co 0
tt- bb Sit!v:J
A 1WMf' no ~
I
132. A square has an area of 16 yds 2. What is the perimeter of the square?
J\~~ If
levi~:.
4~Yt-4t4
0'"
4(4)
=-~
~,~
133. The area of a triangle is 112 m 2. If the length of the base is 16 m, what is the height?
'\1- -=--
~ Ioh
w~~\b~ILl J
Ill.:.
yY\
134. The diagonals of a rhombus are 24 cm and 18 cm long. Find the area of the rhombus.
1:.. ~ I d 1...
\J
-t" 2-4 .,~:-
Pt IlQ vm1-
135. The base of a trapezoid is 10 inches long and the altitude is 20 inches long. If the area is 240 in 2, find the
length of the other base.
I L - ""
A
=-
240
'( b
2-
h
t'~~.J
r\; -::
~(Io .•..x)2.0
=-
l!'"14
\
',Y"I
j
136. Find the area of an equilateral triangle with an apothem 4 cm long and a side 13.8 cm long.
/\.
II =-lOvj)
Oy
A = ~s<'
-
~(Il.'a)"2..
= ~2.~5C"'~
~ t(LtX{f1. tI) '" g'-Z. Ii? tnt't.
~
J5Z=JZz.s
a.~ 1-. 5
\~.
~ -:;..
IS
~
~
CI~
l-.~
138. Find the area of a regular hexagon with an apothem 6 m long. Round your answer to nearest tenth.
~.
.
~ ~~J3
).:. -z. ~
CS\d..t
l.p~c,,()
_
A:.
z~
tt y- 1....:::. 2-S l\' -=-
5'
-=- Z-J"; \-'2.S-~-:.~
J?> ~
~
z.l.f
J3
t,(fo)(~t.(r~)-=. ,,];::.. 1'2. .1-1 ~~
139. Find the area of the circle with equation (x + 2)2+(y - 3)2 = 25
r -= Jz..s -
~
[R 5
\A.~
140. Find the lateral area of a right triangular prism with a height of 30 cm and a right triangular base with a leg
ofl2 em and the hypotennse of 13 em.
~
\
t\.\3
LA -=- -l'rv
=- 30 · ~o -::..A 00
CN\1. 'L
5~
\"2141. Find the total surface area of a right cylinder with a height of 18 in and a radius of 5 in.
~ttr2..
+- ~~
~ \", 57.. \-
rh.,
2 rr S . t ~
~ SO '11'
f- 180 II"
,:,P30 11"' :: 1- 2.Z. • 5 Tin 4
142. A regular pyramid has a slant height of 9 m. The base is a regular hexagon with sides that measure 4 m.
Find the lateral area.
J.. -=- <1
5 =-y
p-::::-
4.~ ~"l..4
-=- -'z., ('L~)( q)
=-[10'0 mi\
143. The lateral area of a right cone is 144JZ" cm. The slant height is 12 cm. Find the total surface area.
Find L.A., S.A., and Volume of each cone, prism, pyramid, occylinder. __
~,
~ Ph., ::QO('I0
45
tr'. IS. 25 :.
S~--315l1' +- rr,~"2-
LA:.
144.
~145.
1.1
05O~'l;
1
5A~2BtPJv
=~.Ti~
={ ('10)'
+40Sd
-::. (P50 (,1..;2,
146.
147.
6
LA- ::.~ P.! -::-i:'IOoll ..
LA -:.2 n-.f.,.' (, ~
l••
a'l1"tb3~
13
~
~'L
16
SA=- L.A
\-"Z..'\T("2.
-::.2. (,4T't
_
10
4 Bt.q.'t- \A.3
Fmdilieme.,nreofoneerleri~:e :e~:p~~o'L~:'~d',lo~. ~
~
10
Sit =- L.J\h", ~u,l.:
I
.• L
V -:..S 6 h. ... ~(too)ti)
-= 4~3.-3
ili~~7t tenilin
necessary.
149)
148)
Find the meaSlU'e of one interior angle in each polygon. ROlUulyour answer to the nearest tendl if
necessmy.
150)
Find dle interior angle SlUnfor each polygon.
152) regular 15-gon
Round your answer to the nearest
('~-i)fBO. ;.1.~lfO.
153) regular 19-9on
154) How many sides does a regular polygon have if each interior angle is 165.6°?
155) How many sides does a regular polygon have if each exterior angle is 8°?
100
tendl if necessary.
t1~
n