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KR KS

;
RT SU
 ________ ~  ______
KR=12, RT = 9, KT = _______,
KS = 16, SU = ________, KU = ________
K
Let
R
S
T
U
1.
18
X = ______
Y
12
Z
Y = _______
15
10
P
Polygons similar as shown
X
12
2.
6
a. Name 2 similar triangles
R
10
Z = ________
b. What postulate justifies your answer
T
15
9
S
3. Q
4. 3 and 27
Find the geometric mean between these 2
numbers.
ABC is a right triangle with altitude
AF . Solve for x, y and z.
A
z
y
x
B
5.
C
F
4
12
Find x, the length of the longer base of
this trapezoid, with a given altitude of 12.
x
12
15
15
10
6.
7. a. 1, 4, 6
b. 7 , 7 , 14
Lengths of triangle are given. Determine
if the triangle formed is acute, right,
obtuse or not possible.
X = _________
45
x
6
Y = _________
45
45
8.
45
y
X = _________
x
8
Y = _________
30
90
45
y
9.
X = _________
6
Y = _________
y
4
45
90
Solve for this trapezoid.
x
10.
X = ____________
x
90
32
22
11.
Y = ___________ degrees
y
90
3
a
12.
a=
Y = ____________
Z
Y
90
34
45
30
Z = ____________
160
13.
A
352
P
14.
B
To find the distance from point A on the
shore of a lake to point B on an island in
the lake, surveyors locate point P with
A  65, P  25, PA  352 . Find AB.
mA  35, mCT  110 , = mBT  _____
B
A
c
Where AT is tangent to the circle
T
15.
With tangent lines shown, find the
measure of angle P.
90
P
16.
Solve for x with secants and tangents as
shown.
4
3
x
17.
X = ____________________
x
4
3
18.
5
x
X represents the length of the whole
segment. Solve for x.
5
6
4
19.
Solve for x.
4
8
6
x
20.
Solve for x.
x
7
6
8
21.
Tangent as shown. Solve for x
6
5
22.
x
Construct segment x such that
1
x
yp
3
y
p
23.
24.
25.
Describe the locus of points in space
that are 4 cm from plane X and 8 cm
from point J
A regular hexagon with perimeter 72
Find the area of the polygon.
Find the area of this equilateral triangle.
1
26.
Find the area of this regular polygon.
1
27.
Find the area of the shaded region.
28.
Given a circle with radius of length 6 and
an inscribed triangle as shown. Find the
total of the shaded regions.
29.
Find the area of the shaded region. 2 is
the distance between the 2 parallel lines
shown. (Assume the white box with the 2
in it is part of the shaded region.)
30.
3
I
II
31.
x
Find the ratio of regions I and II. (x = x
marks congruent angles.)
5
x
2
B
A
E
D
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
C
The area of parallelogram ABCD is 48
square inches, and DE = 2 EC. Find the
area of
a.  ABE
d.  CEF
b.  BEC c.  ADE
e.  DEF f.  BEF
F
A piece of wire 6 inches long is cut
into two pieces at a random point.
What is the probability that both
pieces of wire will be at least 1 inch
long?
Ratio of volumes is 8:125.
A regular square pyramid has a base
edge 30 in and total area 1920 in2.
A cone has volume 8  cubic
centimeters and height 6 cm
The radius of a cylinder is doubled
and its height is halved.
a. Find the volume and total area of
a cube with edge 2k.
b. A cone has radius 8 and height 6.
Find the volume.
(-2, 3) and (3, -2)
36
25
R(4, 3); S(-3, 6); T(2, 1)
( x  7) 2  ( y  8) 2 
Vectors (8, k) and (9, 6) are
perpendicular.
(7, 2) + 3(-1, 0)
44. (1, 1) and (4, 7)
a.What is the scale factor?
b.What is the ratio of heights?
c. What is the ratio of lateral areas?
Find the area of the base, the lateral area
and the slant height.
Find its slant height.
How does the volume change?
c. A cylinder has radius 6 and height 4
cm. Find the lateral area.
d. Find the volume of a sphere with area
9 .
Find the distance between these 2 points
and the slope.
Graph this circle, indicating the center,
radius and 6 points on the circle.
Find the lengths of all three sides of
 RST.
Use the converse of the Pythagorean
Theorem to show that  RST is a right
triangle.
Show two of the sides have perpendicular
slopes by using the products of the slopes.
Find the value of k.
a. Plot each.
b. Solve
Find the equation of a line through these
points.
45. (7, -3)
Find the equation of a vertical line
through this point.
Find the equation of a horizontal line
through this point.
a. Find the equation of the line through
the given point parallel to the line.
b. Find the equation of the line through
the given point perpendicular to the line.
46. (5, 7) and 6x – 2y = 5
47.
4
T
3
2
1
S
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
Q
-2
R
a. Show that QRST is a trapezoid using the numeric coordinates given.
b. Find the equation of the altitude to QT through R.
R (b,c)
(0, 0)
48.
Q(?, ?)
P(a, 0)
Given the parallelogram shown above. Let M be the midpoint of RQ and N be
the midpoint of OP . Use coordinate geometry to prove that ONQM is a
parallelogram.
49. Convert the Cartesian coordinates (5,5 3) and (3, 4) into polar coordinates.
You will need to use a trigonometric ratio for the second coordinate.
50. Find the center and radius of the circle x 2  y 2  6 x  2 y  15  0 .