Download Name__________________________ Geometry Review Unit 1

Name____________________________________
Geometry Review
Unit 1 – Geometry Gallery
STANDARD: LANGUAGE OF MATH ARGUMENT
4. Using the set of numbers below, find the next
two numbers in the set and describe the
pattern.

Deductive Reasoning – Arriving at a conclusion
based on given facts.

Inductive Reasoning – Arriving at a conclusion
based on observations. Uncertain whether
conclusion is actually true.
5. Find a counterexample to the following
conjecture. All odd numbers are prime.

Conjecture – A hypothesis formed by reasoning.

Counterexample – A specific example that
proves a statement false.

Indirect Proof – Based on process of
elimination.
6. Ella factored the first five out of ten trinomials
on a test, and each one factored into a pair
of binomials. She made this statement. “All
of the trinomials on this test will factor into
a pair of binomials.” Determine whether
she made this conclusion based on
inductive or deductive reasoning.

Conditional Statement – “If, then” statement
where the “if” part is the hypothesis and the
“then” part is the conclusion.

Converse – Switch the hypothesis and
conclusion.

Inverse – Negate the hypothesis and
conclusion.

Contrapositive – Switch and negate the
hypothesis and conclusion.
1. It two angles have the same measure, then they
are congruent. You know that
. What can you conclude
about these two angles?
7. Jesse is a girl who loves math class and her dog.
Using this information, what can you
conclude?
a.
b.
c.
d.
Jesse is a boy.
Jesse dislikes math class.
Jesse dislikes her dog.
Jesse is a Justin Bieber fan.
8. Write the converse, inverse, and contrapositive
of the following statement. “If a number is a
natural number, then the number is greater
than zero.”
2. If you study hard, you will pass all your classes.
If you pass all your classes, you will
graduate. What can you conclude from this
information?
Converse:
3. Using the pattern below, sketch the next figure
in the set.
Contrapositive:
Inverse:
STANDARD: PROPERTIES OF POLYGONS

Supplementary – Add up to
.

Complementary – Add up to
.

Sum of Interior Angles -

Sum of Exterior Angles -

Triangle Inequality Theorem – The sum of any 2
sides must be greater than the third side.
.
Rectangle –

Square –

Trapezoid –

Kite –

Special Quadrilaterals –
.

Triangle Congruence Theorems – SSS, SAS, ASA,
AAS, and HL.

Orthocenter – Intersection of 3 altitudes of a
triangle.


Centroid – Intersection of 3 medians of a
triangle.

Circumcenter – Intersection of 3 perpendicular
bisectors of a triangle, circumscribed circle.

Incenter – Intersection of 3 angle bisectors of a
triangle, inscribed circle.

Parallelogram -
9. In
,
,
, and
. Order the sides and angles from
smallest to largest.
10. Determine whether the following sets could be
the lengths of the sides of a triangle.

Rhombus -
a.
b.
c.
d.
12, 13, 25
2, 3, 4
5, 1, 5
49, 51, 99
11. The first four angles in a hexagon each have the
same measure. The other two angles each
measure
more than each of the first four
angles. What is the measure of one of the first
four angles in the hexagon?
12. You are given that
and
. Which side of the triangle has
the shortest length? Which side of the triangle
has the longest length?
16. In the given isosceles trapezoid,
, and
.
What is the length of ?
,
17. What are all the names for quadrilateral
that has its vertices plotted at
,
,
, and
.
18. In the given parallelogram,
. What is the length of
and
?
13. The exterior angles of a pentagon have the
measures
,
, ,
, and
. What is the
measure of the smallest exterior angle?
19. In the given kite,
,
, and
. What is the perimeter of kite
?
14. What are the degree measures of the labeled
interior and exterior angles of this figure?
Justify your answer.
20. Find the values of and in the diagram.
15. Determine the value of for the following
quadrilaterals.
24. Determine the point on the graph that is
equidistant from points , , and .
Unit 2 – Coordinate Geometry
STANDARD: PROPERTIES OF GEOMETRIC FIGURES ON
THE COORDINATE PLANE

Distance Formula –

Midpoint Formula –

Perimeter – Sum of the outside lengths of a
figure.
21. How much further is point
point from point ?
from point
than
22. Line segment
has the endpoints
and
. Point is located at
.
What point on
would create a line segment
with the shortest distance to point ?
25. Parallelogram
has the coordinates
,
, and
. Find the
coordinates of point , and also find the
perimeter of the figure.
26. Points
and
lie on the
coordinate plane. Find the midpoint of segment
.
27. Line segment
is the hypotenuse of a right
isosceles triangle and has coordinate points
and
. What are the possible
locations for vertex ?
23. Find the distance between points
and
.
29. Compare the mean and standard deviations of
the two data sets.
Unit 3 – Statistics
STANDARD: DATA ANALYSIS
Set A: 7, 3, 4, 9, 2
Set B: 5, 8, 7, 6, 4

Mean – Average of the numbers.

Median – Middle number when placed in order
from smallest to largest.

Mode – Most repeated number.

Range – Difference between largest and
smallest numbers.

Box Plot – Min, Q1, median, Q3, max.


30. The table below compares the age of students
in Mrs. June’s 2 classes. Describe the similarities
and differences. Which class has more
variability in their age?
Class 1 Class 2
Mean
12
12
Median
12
11
Mode
10 and 11
13
Range
18
20
Standard Deviation
3.2
2.8
Standard Deviation – Tells us how spread out
the data is.
31. For a large population, the means is 4.8 and the
standard deviation is 3.6. One random sample
produces data values of 5, 1, 3, 4, 7, 6, 8, 2, 1,
and 3. Another random sample produced data
values of 8, 7, 5, 3, 4, 2, 2, 9, 7, and 3. Compare
the means and standard deviations of the
random samples to the population parameters.
32. Find the mean, median, mode, range, variance,
and standard deviation of the data set. If an
outlier is defined as any value more than two
standard deviations from the mean, which, if
any, values in the data would be considered an
outlier? 22, 18, 19, 25, 27, 21, 24, 18, 21, 21, 37
Normal Distribution -
33. Describe a way in which a student could select
people from their high school for a survey using
least biased methods.

Samples – Used when it is impossible collect
data for an entire population. The means and
standard deviations will vary from one sample
to the next.
28. This table below shows the scores of the first
five games played in a professional basketball
league. The winning margin for each game is
the difference between the winning score and
the losing score. What is the mean and standard
deviation of the winning margins for this data?
Winning
Losing
63
61
56
35
61
55
48
30
50
49
34. A data set describing the age of a population of
300 adults is normally distributed with a mean
of 38 and a standard deviation of 4.
a. How many people would be
expected to be older than 46?
b. How many people would be
expected to be between 30
and 42?
Unit 4 – Right Triangle Trigonometry
40. Determine the lengths of the sides labeled
and in the three diagrams below.
STANDARD: SPECIAL RIGHT TRIANGLES

Special Right Triangles –
35. Quadrilateral ABCD is an isosceles trapezoid
with angles A and D measuring
, segment BC
measuring , and segment CD measuring
.
What is the length of segment AD?
36. A square has a side length of 10 cm. What is
the length of the diagonal of the square,
rounded to the nearest whole number?
41. Find the length of the hypotenuse for the
following triangles:
a. A right triangle that has legs with
measures of and
.
37. A 30 ft plank leaning against a building makes
an angle of 60⁰ with the ground. How far from
the base of the building is the plank?
b. A right triangle that has both legs with
measures of 19.
38. The diagonal of a square is
perimeter of the square?
, what is the
39. What kind of triangles are formed when:
a. You cut an equilateral triangle in half.
b. You construct a diagonal in a square?
42. The area of a parallelogram has sides that are
cm and
cm long. The measure of the
acute angles of the parallelogram is
. What
is the area of the parallelogram?
STANDARD: TRIGONOMETRIC RATIOS


Trig Ratios –
Sin =
Cos
=
Tan
48. In a right triangle, if
, what is
?
=
Inverse Trig Ratios – Only used when finding
the angle measure of a right triangle.
49. In right triangle
, if 
acute angles, and
43. What does it mean for two angles to be
complementary?
and 
are the
, what is
?
50. Find the measure of angle . Round your
answer to the nearest degree.
44. Angle and angle are complementary angles
in a right triangle. The value of
is . What
is the value of
?
51. Solve for .
45. Triangle
is a right triangle with right angle
, as shown. What is the area of triangle
?
52. You are given that
. What is the
measure of angle ?
46. A road ascends a hill at an angle of . For every
120 feet of road, how many feet does the road
ascend?
47. Given triangle
, what is
?
53. Solve for .
54. A ladder is leaning against a house so that the
top of the ladder is 18 feet above the ground.
The angle with the ground is 47. How far is the
base of the ladder from the house?
57.
Unit 5 – Circles and Spheres
STANDARD: CIRCLES

Area –

Circumference –

Parts of a Circle –
is tangent to  at point .
measures
12 inches and
measures 7 inches. What is
the radius of the circle?
58. Given  , the

Properties of Tangent Lines –
o Tangent and a radius form a right angle
o You can use Pythagorean Theorem to
find the side lengths
o Two tangents from a common external
point are congruent

Central Angles –

Inscribed Angles –

Angles Outside the Circle –

Intersecting Chords –
and the
find the value of x.
59. If two tangents of  meet at the
external point , find their
congruent length.
60. The measure of
of
?
61. Isosceles triangle
and
measure of
?
is
. What is the measure
is inscribed in this circle.
. What is the
55. What is the value of in this diagram?
56. Given  , with the inscribed quadrilateral, find
the value of each variable.
y
100
T
2x
86
62. In this diagram, segment
is
tangent to circle at point .
The measure of minor arc
is
. What is
?
STANDARD: SPHERES

Surface Area –

Volume -
63. A sphere has a radius of 8 cm. What is the
surface area? Answer in both decimal and
exact -form.
64. A sphere has a surface area of 50 m2. Find the
radius.
69. Find the volume of a hemisphere
which has a diameter of 7.
70. A sphere has a surface area of 81 m2. What
must its diameter be?
71. A balance ball has a surface area of 32 . What
is its volume?
65. A soccer ball has a diameter of 10 in. Find its
volume.
72. A sphere has a diameter of 32 cm.
66. When comparing two different sized
bouncy balls, by how much more is
the volume of larger ball if its radius
is 3 times larger than the smaller
ball?
a. What is the radius?
b. What is the circumference of the great
circle?
c. What is the surface area?
67. A hot air balloon is being deflated.
Its full blown volume is about 80,000
ft3. After 30 minutes, the balloon’s
radius has decreased by . What is
the volume of the balloon at this
time?
68. A sphere has a volume of
cubic
inches. What is the surface area?
d. What is the volume?
73. Find the volume of a hemisphere which has a
radius of 5.
76. Mark buys a car new for $52,000. If the value of
the car depreciates by 12% each year, how
much will the car be worth in 4 years?
Unit 6 – Exponential and Inverses
STANDARD: EXPONENTIAL FUNCTIONS

Properties of Exponents –
o
Product of like bases:
o
Quotient of like bases:
o
Power to a power:
o
Product to a power:
a. Domain:
o
Quotient to a power:
b. Growth or Decay:
o
Zero exponent:
o
Negative exponent:
77. Determine the characteristics of the
exponential function.
c. Range:
or
d. Asymptote:



Solving Exponential Equations –
o Make the bases the same.
o Set the exponents equal and solve for x.
Growth and Decay –
o Growth:
, Decay:
o
Translations –
o Negative : reflects across x-axis
o Negative : reflects across y-axis
o Shifts horizontally by
o Shifts vertically by
74. Solve the exponential equations.
a.
b.
75. Jill invests $6000 at a rate of 4% interest
compounded yearly. Approximately how much
will Jill’s investment be worth in 5 years?
e. Translations:
f.
Y-Intercept:
78. A certain population changes according to the
model
, where represents
the time in years. What is the difference in the
population between years 4 and 8?
79.
Simplify the exponential expressions.
a.
b.
c.
d.
STANDARD: INVERSES OF FUNCTIONS

Inverse of a Function – When x and y values
switch.
o Switch x and y variables.
o Solve for y.

Composition – Verifies that two expressions are
inverses of each other. Substitute one
expression for x in the other expression, the
resulting answer should be x.

Vertical Line Test – Determines whether a
relation is a function.

One-to-One – There is exactly 1 y-value for each
x-value. If a function is 1-to-1, then its inverse is
also a function.

Horizontal Line Test – Determines whether a
function is 1-to-1.
80. If
the domain and range of
, what is
.
84. Using the graph of
below, graph the
inverse of the function. Is
also a
function?
85. Determine whether the functions below are
one-to-one and determine whether the inverses
of the graphed functions are also a function.
a.
81. Find the inverse of the following functions.
a.
83. Using composition, verify that
and
are inverse functions.
b.
b.
82. A table of ordered pairs for a function
shown to the right.
is
a. Write the inverse table.
b. Is
a one-to-one function, why?
c. Is the inverse table a function, why?
86. Using composition,
and
of each other if and only if
equal what?
are inverses
and