Download Analytic Geometry: Final Exam Review

Analytical Geometry: Final Exam Review
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Name __________________
1) Find the measure of RST.
2) EFGH is a parallelogram. Find mE.
3) Find SP.
4) Use the triangle midsegment theorem to find the following lengths:
ST
_____________
PRQ ___________
QR
___________
SUR ___________
PU
___________
SUP ___________
5) Given the partially completed two-column proof, which is the reason for Step 3?
Statements Reasons
= FB
2. FB = EF
3. AE = EF
1. AE
6) If
KLM

1. Given
2. Given
3. ?
RST, find the value of x.
7) In ΔLNR and ΔKMT, given: M

R, T
What is the correct congruence statement?
8) Which similarity postulate or theorem lets
you conclude that JKL
MNO?

9) What is the length of AC ?

N, K
 L, MT = RN, TK = NL, and KM = LR.
10) If lines p and q are parallel, what is the value of x?
11) Name all theorems used to prove triangles are congruent.
12) Name all theorems used to prove triangles are similar.
13) ∆PQS

∆RQS by what theorem?
14) The shadow of a 5-foot boy is 18 feet at the same time the shadow of a building is
99 feet. How tall is the building?
15) The coordinates of a triangle are K(-4, 8), L(0, 6), and M(-1, -7). What are the coordinates of the
image of M after a dilation with scale factor 0.8?
16) Polygon K(2, 3), L(4, 5), M(3, 7) was mapped to polygon N(10, -2.5), O(15,2.5), P(12.5, 7.5). First by
the translation: (x, y) → (x + 2, y - 4). And then by which dilation?
17) If j
k, solve for x and find the measure of both angles.
18) Which angle is a supplement of RPS?
Which two angles are vertical angles?
19) Ray BD bisects ABC. If mABD = 2x + 30 and mDBC = 6x – 10, find x, mABC, and mABD.
20) List all corresponding angles.
List all vertical angles.
List all alternate interior angles.
List all alternate exterior angles.
List all same side exterior angles.
21) Circle the correct answer:
Vertical angles are (congruent/supplementary).
Corresponding angles are (congruent/supplementary).
Alternate interior angles are (congruent/supplementary).
Same side interior angles are (congruent/supplementary).
Same side exterior angles are (congruent/supplementary).
22) Name the triangle and find the measure of the missing angle.
23) What is the value of x?
24) The figure represents a rectangular gate with diagonal braces. To the nearest tenth, what is the
width, QT, of the gate?
25)
Find the hypotenuse. Then list all of the trig ratios
for A.
9
A
½ , find the values of the other trig functions.
26)
If the sin  =
27)
If tan  = 4, find sin  and cos  .
40
28)
Given: BA = BD, BE = BC
Prove: ∆ABE  ∆DBC
Proof:
Statements
Reasons
1. a. ______________________ 1. Given
2. b. ______________________ 2. Vertical Angles Thm.
3. ∆ABE  ∆DBC
3. c. ______________________
29) Apply the rigid transformation: M(x, y) → (
x - 2,y + 1). Name the transformation.
30) Apply the rigid transformation: M(x, y) → (-x, -y). Name the transformation.
31) Triangle ABC is an isosceles right triangle. Find the following:
Side length if the hypotenuse is 4.
_______
32) Triangle PQR is a right triangle with a 60° angle. If PR is the hypotenuse, find the following:
Short leg if PR is 10.
________
Long leg if PR is 8.
________
PR if the long leg is 6. ________
A
33) Find each of the following for the given right triangle:
1.
2.
3.
4.
Sin A
Cos A
Tan B
mB
__________
__________
__________
__________
?
1
5
C
34). Solve for x in each of the following right triangles.
x
27
1
9
3
8
68
9
4
x
x
60
3
2
5
4
2 1
1
x
49
x
B
2
0
x
x
4
1
6
1
Y
x
1
4
4
7
30
8
1
2
7
x
60
y
y
35) Complementary angles are two angles ____________________________________.
Supplementary angles are two angles ____________________________________.
36) Write each trig function in terms of its cofunction.
Example A: sin 24˚ = cos 66˚
b) sin 48˚
c) cos 45˚
Simplify completely.
37)
 121
38)
4  50
39)
-2i
 144
d) cos 19˚
40)
(-5 + 2i) + (6 + 7i)
41)
(10 – 8i) – (-2 + 3i)
42)
(6 – 3i) – (-2 + i)
43)
6i (-4i)2
45)
3i
9  2i
1  2i
5i
44)
46)
(5 – i)(3 + 2i)
47)
(3i)3
48)
2i (-5 + 6i)
49)
(2 + 3i)2
50) Classify the following polynomials by degree and number of terms :
____________
____________
____________
____________
____________
____________
____________
____________
Name by
Degree
A. Constant
B. Linear
C. Quadratic
D. Cubic
2x3 – 7x2 + 13
8
-5x2 – 3x + 1
6x - 4
Simplify the following polynomials.
51) 4 x  2 x  3x  5 x  6 x
3
2
52)
3
(5x 3  2 x )  (7  4 x 3 )  ( x  5)
53)
(7m 3 )( 2m)
54) (7 x  4)( 2 x  6)
55)
(3x  5) 2
56)
57) (2x3 + 9x2 -4x + 5) (x + 5)
Name by No. of
Terms
G. Monomial
H. Binomial
I. Trinomial
J. Polynomial
( x  3)(2 x 2  4 x  1)
58) (4x3 + 1) (x – 2)
59) Use the figure to answer the following. Point P is the center of the circle.
mOD  __________
mEL= ____________
mPD  __________
S
6
6
D
x = __________
x
mIE=62°
mHD  6
E
3
6
P
L
O
60) Find the measure of the angle marked x.
67°
61) If VS is a diameter for U, mRV = 30 ° and mSW = 70°, find mT.
mT = __________
I
H
mPDH = __________
S
W
T
U
V
R
62) Find the length of the radius of the circle if AB is a tangent for the circle. (Show work.)
B
r = __________
AC  13
12
A
C
63) Find the length of x in the following figures. Show how you set up your problems.
x = __________
x = __________
8
5
4
4
3
6
x
x
x = __________
x = __________
4
12
13
x
6
9
x = __________
x = __________
6
2
x
5
9
16
C
64) Given AE = x, BE = x – 2, CE = 3
and DE = 8, find x.
A
B
E
x = __________
D
65) Refer to the figure below. Find mFG.
mFG = __________
C
F
(2x-7)°
84°
G
(4x+7)°
D
x
x
Find the measure of the variable(s) in the following. Show your work.
66) mFG = 170°, mEDG = 55°
67) mIJ = 46°, mHGI = 116°
x = __________
x = __________
H
F
I
x
G
E
x
D
J
K
G
68a) x = __________
68b) x = __________
y = __________
100°
°
y = __________
104°
x
67°
z = __________
y
z
y
110°
°
75°
69) In circle O, AB is a diameter and the measure of arc BC is 60.
a. Find the measure of arc CAB, the area of the shaded region. and the length of arc CB.
b. Suppose AOC was the shaded region. Find the area of that region and the length of arc AC.
70) Find the area of H.
71) Find the diameter of H.
x
72) Find the surface area and volume of a sphere with r = 6.
73) If the surface area of a sphere is 300  , what is the radius?
74) If the volume of a sphere is 288  , what is the diameter of the sphere?
75-70: Find the Surface area and Volume for each of the following figures.
75. V = _____________
76. V = _____________
SA = ___________
SA = ___________
77. V = _____________
79. V = _____________
SA = ___________
80.. V = _____________
81) In parallelograms, opposite sides are ________________ and diagonols are _________________.
82) In similar triangles, sides are __________________ and angles are ____________________.
83) Give 3 different types of rigid motion: _______________, _______________, and ________________.