Download Geometry EOI Practice 1. By the Law of Syllogism, what statement

Geometry EOI Practice
PASS 1.1: Identify and use logical reasoning skills (inductive and
deductive) to make and test conjectures, formulate counter examples, and
follow logical arguments.
1. By the Law of Syllogism,
what statement follows from
the following pair of true
statements?
Use the following statements for
exercises 3 and 4.
p: If a rectangle is a rhombus,
then the rectangle is a square.
q: If a rectangle is a square, then
the rectangle is a rhombus.
r: If a rectangle is not a
rhombus, then the rectangle
is not a square.
s: If a rectangle is not a square,
then the rectangle is not a
rhombus.
1.1
If Nate eats chips, then he
uses salsa dip.
If Nate uses salsa dip, then he
gets indigestion.
a. Nate uses salsa dip.
b. Nate gets indigestion.
c. If Nate uses salsa dip, then
he gets indigestion.
d. If Nate eats chips, then he
gets indigestion.
3. Which statement is truth
1.1 functionally equivalent to q?
a. p
c. s
b. r
d. none
2. Which statement is logically
1.1 equivalent to the statement,
“If we recycle, then the
amount of trash in landfills is
reduced”?
a. If we do not recycle, then
the amount of trash in
landfills is not reduced.
b. If the amount of trash in
landfills is reduced, then
we recycled.
c. If the amount of trash in
landfills is not reduced,
then we did not recycle.
d. If we do not recycle, then
the amount of trash in
landfills is reduced.
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4. Which statements are true?
a. p and s only
c. none
b. q and r only
d. all
1.1
1
Geometry EOI Practice
5. What logical conclusion can
1.1 be made from the following
statements?
7. Use the statement below to
1.1 answer the following
question.
• If Delphie has sugar in her
cupboard, then she can
make apple pie.
• Delphie has sugar in her
cupboard.
• All fruits grow on trees.
Which proves the statement
false?
a. Oranges are fruits.
Oranges grow on trees.
b. Acorns grow on trees.
Acorns are not fruits.
c. Strawberries are fruits.
Strawberries do not grow
on trees.
d. Potatoes are not fruits.
Potatoes do not grow on
trees.
a. Delphie just bought some
sugar.
b. Apples make good pie.
c. Delphie can make apple
pie.
d. Apple pie is made with
sugar
6. The following statements are
1.1 true:
8. Make a conjecture about the
1.1 next term in this sequence:
92, 87, 82, 77, 72.
• If the phone rings, Antoine
will answer it.
• If Antoine answers the
phone, he will have to take
a message.
• Antoine has not taken any
messages.
a. -5
b. 62
Which statements must be
true?
9. Given: a + b ≤ 8and a = 2
1.1 Conjecture: b ≤ 5
a. The phone has not rung.
b. Antoine does not have any
paper.
c. Antoine has answered the
phone.
d. The phone has been busy
all day.
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c. 67
d. 77
Which of the following
would be a counterexample?
a. b = 3
b. b = 5
2
c. b = 6
d. b = a
Geometry EOI Practice
12. Marcus is on the track team.
1.1
He participates in the high
jump and the 100-meter
race, but does not
participate in the 4-person
relay. In which section of
the diagram below should
Marcus be placed?
10. “Two lines in a plane
1.1 always intersect in exactly
one point.”
Which of the following best
describes a counterexample
to the assertion above?
a. Coplanar lines
b. Parallel lines
c. Perpendicular lines
d. Intersecting lines
11. Which figure can serve as a
1.1
counterexample to the
conjecture below?
• If one pair of opposite
sides of a quadrilateral is
parallel, then the
quadrilateral is a
parallelogram.
a. Rectangle
b. Rhombus
c. Square
d. Trapezoid
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3
a. A
b. B
c. C
d. D
a. A
c. C
b. B
d. D
Geometry EOI Practice
13. Alice, Bob, Colleen, and
1.1
Dave are in line at a grocery
store. Each needs to buy a
different item. The items
are bread, cereal, milk, and
fruit.
14. Jeff, Kim, Hans, and Lou
1.1 each have a different pet: a
dog, a turtle, a parrot, and a
snake. Jeff is teaching his
pet to speak. Kim’s pet has
four legs. Hans’ pet has no
legs. Lou’s pet has more
legs than Jeff’s pet but no
fur. Who owns the dog?
1. Bob was second inline,
after the person who
bought milk but before
the person who bought
the bread.
2. Colleen did not buy the
fruit.
3. Alice bought the cereal.
4. Dave was the first person
in line.
Based on the statements,
who bought the loaf of
bread?
a. Alice
c. Colleen
b. Bob
d. Dave
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4
a. Jeff
c. Hans
b. Kim
d. Lou
Geometry EOI Practice
PASS 1.2: State, use, and examine the validity of the converse, inverse, and
contrapositive of “if-then” statements.
1. Which statement is the
1.2 converse of a → b ?
4. Which statement is the
1.2 inverse of “If it rains, then I
do not go fishing”?
a. b → a
b. a → ∼ b
c. ∼ a → ∼ b
d. ∼ b → ∼ a
a. If I do not go fishing, then
it rains.
b. If it does not rain, then I
go fishing.
c. If it rains, then I go
fishing.
d. If I go fishing, then it does
not rain.
2. What is the converse of the
1.2 statement “If x is even, then
x + 1 is odd”?
5. What is the contrapositive of
1.2 the statement q → ∼ p ?
a. If y is even, then y + 1 is
odd.
b. If x is not even, then x + 1
is odd.
c. If x is odd, then x + 1 is
even.
d. If x + 1 is odd, then x is
even.
a.
b.
c.
d.
∼ p→q
p→ ∼q
6. Which is the contrapositive
1.2 of ∼ p → q ?
3. Which is the converse of the
1.2 statement “If today is
Presidents’ Day, then there is
no school”?
a.
b.
c.
d.
a. If today is Presidents’
Day, then there is school.
b. If there is school, then
today is not Presidents’
Day.
c. If there is no school, then
today is Presidents’ Day.
d. If today is not Presidents’
Day, then there is school.
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∼q→ p
∼ p→q
5
∼q→ p
p→ ∼q
q→ ∼ p
∼ p↔q
Geometry EOI Practice
Use the following statements for exercises 7-10.
p: If a rectangle is a rhombus, then the rectangle is a square.
q: If a rectangle is a square , then the rectangle is a rhombus.
r: If a rectangle is not a rhombus, then the rectangle is not a square.
s: If a rectangle is not a square, then the rectangle is not a rhombus.
7. Which statement is the
1.2 inverse of p?
a. p
b. q
9. Which statement is the
1.2 contrapositive of q?
c. r
d. s
a. p
b. q
8. Which statement is the
contrapositive of p?
10. Which statement is the
1.2 inverse of r?
1.2
a. p
b. q
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c. r
d. s
c. r
d. s
a. p
b. q
6
c. r
d. s
Geometry EOI Practice
PASS 2.2a: Use the angle relationships formed by parallel lines cut by a
transversal to solve problems.
4. Given
For Questions 1-5, refer to the
following figure. Identify the
special name for each angle pair.
2.2a
s t and m∠1 = 8 x − 4 and m∠15 = 6 x + 24, find x.
a. -10
b. 14
5. If s t by the Alternate Exterior
2.2a Angles Theorem, which angle
pair must be congruent?
1. ∠1 and ∠5
a. ∠1 and ∠7
b. ∠1 and ∠5
2.2a
a.
b.
c.
d.
c. 20
d. 28
alternate exterior
alternate interior
consecutive interior
corresponding
c. ∠1 and ∠15
d. ∠1 and ∠13
6. Which of the following is not
2.2a true when a b ? Refer to the
following figure.
2. ∠10 and ∠14
2.2a
a.
b.
c.
d.
alternate exterior
alternate interior
consecutive interior
corresponding
a.
b.
c.
d.
3. Given s t and m∠7 = 84, find m∠10.
2.2a
a. 6
b. 84
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c. 96
d. 104
7
∠1 ≅ ∠5 and ∠4 ≅ ∠8
m∠2 = m∠6
m∠1 + m∠5 = 180°
m∠4 + m∠6 = 180°
Geometry EOI Practice
7. Which of the statements must be
2.2a true if a b and x y ? Refer to the
following figure.
9. In the figure shown below, lines
2.2a l and m are parallel.
I. m∠1 = m∠5
II. m∠3 + m∠5 = 180°
III. m∠7 + m∠8 = 180°
What is the value of x?
a. I only
b. II only
a. 20°
b. 60°
c. III only
d. I and III
8. If m∠4 = 50° and b c , then which
2.2a statement is true? Refer to the
following figure.
a. m∠6 = m∠10
b. m∠8 = 50°
10. In the figure shown below,
2.2a lines l and m are parallel and
line t is a transversal.
Which pair of angles must be
supplementary?
c. m∠8 = m∠7
d. m∠6 = 60°
a. ∠1 and ∠6
b. ∠3 and ∠5
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c. 80°
d. 100°
8
c. ∠3 and ∠7
d. ∠4 and ∠5
Geometry EOI Practice
11. A construction engineer needs to make sure a ceiling beam is parallel to
2.2a its corresponding floor beam. Using the drawing below as a guide,
which pair of measurements is sufficient to show the beams are
parallel?
Which pair of angles must be supplementary?
a. x = z
b. y = w
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c. x = y
d. y = z
9
Geometry EOI Practice
PASS 2.2b: Use the angle relationships formed by two lines cut by a transversal
to determine if the two lines are parallel and verify, using algebraic and
deductive proofs.
3. If m∠6 = 10 x − 6 and m∠11 = 4 x + 18,
2.2b find x so that s t.
For Questions 1-3, refer to the
figure below. Identify the special
name for each angle pair.
a. 2
b. 4
c. 12
d. 32
4. Which postulate or theorem
y.
2.2b would prove x
1. Given ∠6 ≅ ∠12, which postulate
2.2b or theorem justifies that s t ?
a. Corresponding Angles
Postulate
b. Consecutive Interior Angles
Theorem
c. Alternate Exterior Angles
Theorem
d. Alternate Interior Angles
Theorem
a. Consecutive Interior Angles
Converse
b. Corresponding Angles
Converse
c. Alternate Interior Angles
Converse
d. Alternate Exterior Angles
Converse
2. If ∠8 ≅ ∠16, which postulate or
2.2b theorem justifies that s t ?
a. Corresponding Angles
Postulate
b. Consecutive Interior Angles
Theorem
c. Alternate Exterior Angles
Theorem
d. Alternate Interior Angles
Theorem
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10
Geometry EOI Practice
5. Which postulate or theorem
y.
2.2b would prove x
7. Which lines are parallel?
2.2b
a. Consecutive Interior Angles
Converse
b. Alternate Interior Angles
Converse
c. Alternate Exterior Angles
Converse
d. Cannot prove x y with given
information
a. EB FD
c. EF BC
b. AE CF
d. both b and c
8. Complete the following to make
2.2b a true statement. “In a plane, if
two lines are _?_ to the same
line, then they are _?_ to each
other.”
a.
b.
c.
d.
6. What value of x would make
2.2b lines w and v parallel?
perpendicular, parallel
perpendicular, perpendicular
parallel, parallel
both a and c
9. Determine which lines must be
2.2b parallel.
a. 30
b. 20
c. 60
d. 40
a. a b
b. c d
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11
c. c e
d. both a and c
Geometry EOI Practice
Use the figure below for
Exercises 12-13.
10. What value of x makes a b ?
2.2b
a. 10
b. 30
c. 50
d. 70
12. If m∠1 = m∠9, then which two
2.2b lines are parallel?
11. Which best describes the
2.2b relationship of the lines shown
below?
a. b d
b. b c
c. a d
d. c d
13. If m∠6 = 85° and m∠4 = 95° ,
2.2b then the following conclusion
can be made:
a. a ⊥ d
b. b c
a. a ⊥ b
b. c a
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c. b a
d. b c
12
c. d c
d. b d
Geometry EOI Practice
PASS 2.2c: Use relationships between pairs of angles (for example, adjacent,
complementary, vertical) to solve problems.
1. Find m∠BDC.
4. Which angles are
2.2c supplementary?
2.2c
a. ∠1 and ∠4
b. ∠4 and ∠5
a. 185°
b. 115°
c. 25°
d. 175°
c. ∠1 and ∠5
d. B and C
5. What is the m∠1?
2.2c
Refer to the diagram below
for Exercises 2-4.
a. 45°
b. 90°
c. 55°
d. 145°
6. Find the value of x.
2.2c
2. Which angles are a linear
pair?
2.2c
a. ∠1 and ∠2
b. ∠2 and ∠3
c. ∠1 and ∠4
d. ∠4 and ∠5
a. 13.3
b. 7
7. Two angles are
2.2c complementary. One angle
has a measure that is twice
the other angle. What is the
measure of the smaller angle?
3. Which angles are vertical
2.2c angles?
a. ∠1 and ∠2
b. ∠1 and ∠5
c. ∠3 and ∠5
d. ∠1 and ∠4
a. 15
b. 30
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c. 14
d. 26
13
c. 45
d. 60
Geometry EOI Practice
11. If m∠ABD = 56, find m∠DBC .
8. Find the value of y.
2.2c
2.2c
a. 10
b. 28
c. 20
d. 152
a. 124
b. 56
9. What is the measure of
2.2c the diagram?
a. 3°
b. 39°
∠x
in
12. If m∠AFB = 5 x − 10 and
2.2c m∠BFC = 3 x + 20, find x .
c. 5°
d. 65°
a. 10
b. 15
right
complementary
vertical
supplementary
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c. 21.25
d. 23.3
13. Two boards are being cut at
2.2c angles to ensure a tight fit.
If one board is cut at a 140°
angle, what must the acute
angle of the other board
measure to form the tight
fit?
10. To solve for x, what angle
2.2c relationship would you use?
a.
b.
c.
d.
c. 44
d. 34
a. 40°
b. 90°
14
c. 60°
d. 140°
Geometry EOI Practice
17. Which pair of angles are not
2.2c adjacent?
For Questions 14-16, use the
figure below
a. ∠1and ∠2
b. ∠3 and ∠4
14. Which pair of angles are
2.2c vertical angles?
a.
b.
c.
d.
∠RST , ∠TSU
∠RSX , ∠TSU
∠TSU , ∠USV
∠RSX , ∠XSW
18. Use the diagram to find
2.2c m∠FDG.
15. Which angle is
2.2c supplementary to ∠USV ?
a. ∠TSU
b. ∠VSW
c. ∠2 and ∠3
d. ∠1 and ∠4
a. 15°
b. 120°
c. ∠RSV
d. ∠WSR
c. 150°
d. 130°
19. In the diagram, what are the
2.2c values of x and y?
16. Find x and y.
2.2c
a.
b.
c.
d.
x = 10, y = 12
x = 20, y = 7
x = 10, y = 8
x = 50, y = 40
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a. x = 47, y = 75
b. x = 47, y = 74
15
c. x = 75, y = 47
d. x = 71, y = 51
Geometry EOI Practice
PASS 2.3a: Identify, describe, and analyze polygons (for example, convex,
concave, regular, pentagonal, hexagonal, n-gonal).
1. A triangle with three acute
2.3a angles and no congruent
sides is _?_ .
a.
b.
c.
d.
4. The triangle below can be
2.3a classified as _?_ .
an equiangular triangle
a right triangle
an isosceles triangle
an acute scalene triangle
a.
b.
c.
d.
2. A triangle with side lengths
2.3a of 5 cm, 3 cm, and 5 cm is
_?_ .
a.
b.
c.
d.
an equilateral triangle
an obtuse triangle
an isosceles triangle
an acute triangle
acute isosceles
acute scalene
obtuse isosceles
obtuse scalene
5. Which of the following is not
2.3a a polygon?
3. The triangle below can be
2.3a classified as _?_ .
a.
c.
b.
d.
6. A polygon with seven sides is
2.3a called a(n)
a.
b.
c.
d.
a. octagon
b. decagon
acute isosceles
acute scalene
obtuse isosceles
obtuse scalene
7. If a polygon is both
2.3a equiangular and equilateral,
how should it be classified?
a. regular
b. right
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c. heptagon
d. hexagon
16
c. congruent
d. irregular
Geometry EOI Practice
8. Which describes this figure?
11. Which figure is not a
2.3a polygon?
2.3a
a.
a. hexagon, concave, not
regular
b. pentagon, concave, regular
c. hexagon, convex, not
regular
d. not a polygon
b.
c.
d.
12. Which figure is not a
2.3a convex polygon?
a.
b.
c.
d.
9. If m∠L = 45 and m∠M = 45, LMN
2.3a is classified as what kind of
triangle?
a.
b.
c.
d.
13. Which figure is not a
2.3a regular polygon?
acute scalene
obtuse isosceles
acute isosceles
right isosceles
a.
10. The figure shown below can
2.3a be classified as which of the
following?
a polygon
II. a quadrilateral
III. a hexagon
IV. an octagon
I.
a.
b.
c.
d.
I, II, IV
II
III
I, IV
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17
b.
c.
d.
Geometry EOI Practice
14. The figure is an example of
2.3a _?_ .
a. hexagon
b. heptagon
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15. What type of triangle is
ABC ?
2.3a
a.
b.
c.
d.
c. octagon
d. nonagon
18
acute isosceles
right scalene
right isosceles
obtuse scalene
Geometry EOI Practice
PASS 2.3b: Apply the interior and exterior angle sum of convex polygons
to solve problems, and verify using algebraic and deductive proofs.
4. What is the measure of an
2.3b exterior angle of regular
pentagon?
1. An exterior angle at the base
2.3b of an isosceles triangle
measures 110°. What is the
measure of the vertex angle?
a. 55°
b. 110°
a. 51.4°
b. 72°
c. 108°
d. 144°
c. 70°
d. 40°
5. Find the measure of ∠A .
2.3b
2. Each exterior angle of a
2.3b certain regular polygon
measures 30°. How many
sides does the polygon have?
a. 6
b. 9
c. 10
d. 12
a. 45°
b. 55°
6. The diagram below has a
2.3b triangular area. What are the
measures of the 3 angles
inside the triangle?
3. What is the measure of ∠A in
2.3b the regular polygon?
a. 45°
b. 120°
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c. 58°
d. 85°
c. 135°
d. 145°
a.
b.
c.
d.
19
90°, 50°, 40°
90°, 60°, 30°
90°, 45°, 45°
110°, 50°, 20°
Geometry EOI Practice
7. A regular polygon has an
2.3b interior angle with a measure
of 135°. How many sides
does the polygon have?
a. 5
b. 6
11. In triangle ABC shown
2.3b below, m∠A = 60° and m∠C=80°.
The exterior angle at B
measures (x + 10)°.
What is the value of x?
c. 7
d. 8
8. What is the value x?
2.3b
a. 30
b. 50
a. 45
b. 50
12. Mary is designing a garden
2.3b in the shape of a regular
octagon. She intends to
surround the garden with a
border of rocks as shown in
the figure below. At what
angle should the sections of
the border intersect?
c. 55
d. 60
9. What is the number of sides
2.3b of a polygon if the sum of the
measures of its angles is
1260°?
a. 5
b. 6
c. 130
d. 140
c. 7
d. 9
10. What is the number of sides
2.3b of a polygon if the sum of
the measures of its angles is
4140°?
a. 25
b. 23
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a. 45°
b. 60°
c. 21
d. 24
20
c. 120°
d. 135°
Geometry EOI Practice
16. What are the values of x,
2.3b and y?
13. What is the sum of the
2.3b measures of the exterior
angles of a decagon?
a. 1440°
b. 1080°
c. 360°
d. 720°
14. Find the sum of the
2.3b measures of the interior
angles of a convex 50-gon.
a. 9000
b. 8640
a.
b.
c.
d.
c. 360
d. 172.8
15. Find x.
x = 91°, y = 98°
x = 91°, y = 108°
x = 101°, y = 98°
x = 101°, y = 108°
17. In the diagram,
2.3b ∆ABC and ∆RST are
congruent equilateral
triangles with corresponding
sides parallel.
2.3b
What is the value of x?
a. 16
b. 34
c. 50
d. 70
a. 90°
b. 120°
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21
c. 135°
d. 144°
Geometry EOI Practice
18. The measures of some
2.3b angles are given in this
figure. What is the measure
of ∠N ?
a. 40°
b. 58°
20. Figure ABCDEFGH is a
2.3b regular octagon. What is
the measure of ∠DCQ ?
c. 82°
d. 122°
a. 135°
b. 60°
19. In the figure, the measure of
2.3b ∠CAD is twice the measure
of ∠CAB . What is the
measure of ∠CAB ?
a. 120°
b. 60°
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c. 45°
d. 30°
21. The measures of some
2.3b angles are given in the
figure. What is the value of
x?
c. 45°
d. 30°
a. 65
b. 70
22
c. 80
d. 85
Geometry EOI Practice
22. The polygon shown is
2.3b convex. The sum of its
interior angle measures is
_?_
25. Find the value of x.
2.3b
a. 21
b. 25
a. 900°
b. 1,260°
26. The sum of the interior
2.3b angles of a polygon is the
same as the sum of its
exterior angles. What type
of polygon is it?
c. 1,620°
d. 2,520°
23. Which angle measure below
2.3b is not a possible measure of
an exterior angle of a
regular polygon?
a. 36°
b. 40°
c. 28
d. 31
a. quadrilateral c. octagon
b. hexagon
d. decagon
c. 45°
d. 54°
27. In the figure, TIL overlaps
RAN. RIG is formed.
2.3b
What is the m∠c in RIG?
24. In the figure, what is the
measure of ∠C ?
a. 70°
b. 90°
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c. 100°
d. 110°
a. 30°
b. 55°
23
c. 85°
d. 95°
Geometry EOI Practice
PASS 2.3c: Develop and apply the properties of quadrilaterals to solve
problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).
1. What are the values of the
2.3c variables in quadrilateral
MNOP?
a.
b.
c.
d.
x = 4,
x = 6,
x = 5,
x = 7,
y
y
y
y
=
=
=
=
4. KLMN is a parallelogram.
2.3c Which of the following
statements is false?
19
19
27
26
a. KP = MP
b. LP = NP
5. If ∠D ≅ ∠F and ∠E and ∠F are
2.3c supplementary, then you
know that DEFG must be
what type of special
quadrilateral?
2. NPQR is a trapezoid and ST
2.3c = 24. Find the value of x.
a. 6
b. 10
c. 8
d. 9
a. parallelogram c. rhombus
b. square
d. rectangle
3. ABCD is a parallelogram.
2.3c Find m∠C .
a. 57°
b. 66°
Moore Public Schools
Geometry EOI Practice
c. LM = KN
d. LN = KM
6. Which quadrilateral is a
2.3c parallelogram?
c. 76°
d. 114°
24
a.
c.
b.
d.
Geometry EOI Practice
7. Which of the following terms
2.3c could not be used to describe
the figure below?
10. Find m∠1 in parallelogram
2.3c ABCD.
a. 19
b. 38
c. 52
d. 56
a. parallelogram c. rectangle
b. square
d. quadrilateral
11. ABCD is a parallelogram
2.3c with diagonals intersecting
at E. If AE = 4x – 8 and
EC = 36, find x.
8. What is the length of the
2.3c midsegment of trapezoid
ABCD?
a. 7
b. 11
a. 6
b. 8
c. 9
d. 15
c. 15.5
d. 38
12. Find x and y so that this
2.3c quadrilateral is a
parallelogram.
9. Which of the following
2.3c statements is never true?
a. A trapezoid is a rectangle.
b. A rectangle is a
parallelogram.
c. A parallelogram is a
rhombus.
d. A square is a rhombus.
Moore Public Schools
Geometry EOI Practice
a.
b.
c.
d.
25
x=
x=
x=
x=
27,
27,
13,
13,
y
y
y
y
=
=
=
=
90
40
90
40
Geometry EOI Practice
13. Find x so that this
2.3c quadrilateral is a
parallelogram.
a.
7
1
3
b. 8
16. EF is the median of
2.3c isosceles trapezoid ABCD.
Find x.
c. 12
a. 2x - 46
b. 32
d. 66
17. Given rhombus ABCD, find
2.3c m∠1.
14. The diagonals of square
2.3c ABCD intersect at E. If AE
= 2x + 6 and BD = 6x – 10,
find AC.
a. 11
b. 28
c. 46
d. 68
c. 56
d. 90
a. 45
b. 60
c. 90
d. 120
15. For isosceles trapezoid
2.3c MNOP, find m∠MNP.
18. In trapezoid DEFG, find
2.3c m∠D.
a. 44
b. 64
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Geometry EOI Practice
c. 80
d. 116
a. 44
b. 72
26
c. 108
d. 136
Geometry EOI Practice
19. Given trapezoid ABCD with
2.3c median EF , which of the
following is true?
22. Given: TRAP is isosceles
2.3c trapezoid with diagonals RP
and TA . Which of the
following must be true?
a. RP ⊥ TA
b. RP TA
a. EF =
1
2
AD
b. AE = FD
c. RP ≅ TA
d. RP bisects TA
c. AB = EF
d. EF =
BC + AD
23. What values of a and b
2.3c make quadrilateral MNOP a
parallelogram?
2
20. Quadrilateral ABCD is a
2.3c parallelogram. Which of
the following must be true?
a. a = 1, b = 5
b. a = 5, b = 1
a. AB ≅ AD
b. AC ≅ BD
c. ∠A ≅ ∠D
d. ∠B ≅ ∠D
c. a =
11
d. a =
34
7
7
,b=
34
,b=
11
7
7
21. ABCD is a rhombus. What
2.3c is the measure of ∠CBD ?
24. Choose the statement that is
2.3c true about a kite.
a. 50°
b. 60°
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Geometry EOI Practice
a. Only one pair of opposite
angles are congruent.
b. Opposite sides are
congruent.
c. Diagonals bisect each
other.
d. Diagonals are congruent.
c. 70°
d. 75°
27
Geometry EOI Practice
PASS 2.3d: Use properties of 2-dimensional figures and side length, perimeter
or circumference, and area to determine unknown values and correctly
identify the appropriate unit of measure of each.
1.
2.3d
2.
2.3d
3.
2.3d
A rectangle has an area of
150 ft 2 and a perimeter of
50 ft. What are the
dimensions of the
rectangle?
4.
2.3d
The area of a circle is the
same as the area of a square
whose sides measure 6
centimeters. The radius of
the circle is closest to:
a. 75 ft by 2 ft
a. 4 centimeters
b. 30 ft by 5 ft
b. 3 centimeters
c. 15 ft by 10 ft
c. 5 centimeters
d. 50 ft by 3 ft
d. 6 centimeters
Rhombus ABCD has an area
of 264 square units.
If DB = 12 units, find AC.
a. 44 units
c. 18 units
b. 22 units
d. 12 units
5.
2.3d
What is the height of a
parallelogram with a base of
9 centimeters and an area of
36 square centimeters?
a. 6 centimeters
b. 4 centimeters
c. 2 centimeters
d. 9 centimeters
Moore Public Schools
Geometry EOI Practice
28
The circumference of the
plate shown below is 84.5
cm. To the nearest
hundredth, what is the
plate’s diameter?
Use π = 3.14.
a. 5.19 cm
c. 13.46 cm
b. 10.38 cm
d. 26.91 cm
Geometry EOI Practice
6.
2.3d
7.
2.3d
8.
2.3d
A square with an area of 64
square inches has a
perimeter of _?_
9.
2.3d
The circumference of a circle is
divided by 2π . What is the
result?
a. 64 in.
c. 32 in.
a. r 2
c. 2r
b. 16 in.
d. 128 in.
b. r
d. π
A triangle has an area of 72
square feet and a height of 9
feet. Find its base.
a. 16 ft
c. 32 ft
b. 8 ft
d. 9 ft
10. The center of a circle is located
at ( −4, 0 ) . Point ( 0, 0 ) lies on
2.3d
the edge of the circle. What is
the circumference of the circle?
The perimeter of an
equilateral triangle is 18.
What is the length of each
altitude of the triangle?
a. 3 3
c. 12
b. 6
d. 6 3
Moore Public Schools
Geometry EOI Practice
29
a. 16π
c. 8π
b. −4π
d. 4π
Geometry EOI Practice
PASS 2.4a: Determine and verify the relationships of similarity of triangles,
using algebraic and deductive proofs.
1. Which statement is true about
2.4a the triangles?
3. Which of the following
2.4a statements is true about the
triangles below?
a. ABC ∼ DEF by AA.
b. ABC ∼ DEF by SSS.
c. ABC ∼ DEF by SAS.
d. The triangles can not be
proven similar.
a. QRS ∼ TUV by AA.
b. QRS ∼ TUV by SSS.
c. QRS ∼ TUV by SAS.
d. The triangles can not be
proven similar.
2. Which triangle is similar to
ABC ?
2.4a
4. In QRS , TU RS . Which of
2.4a the following statements is
not true by the Side-Splitting
Theorem?
C
a.
c.
b.
d.
a.
b.
Moore Public Schools
Geometry EOI Practice
30
QT
TR
TR
QR
=
QU
=
US
US
QS
c.
d.
QT
QS
QT
QU
=
QU
=
QR
TR
US
Geometry EOI Practice
5. Use the Side-Splitting
2.4a Theorem to find x.
a. 2.5 units
b. 6.4 units
8. Find the triangle similar to
ABC below.
2.4a
a.
c.
b.
d.
c. 7 units
d. 10 units
6. Using the Side-Splitting
2.4a Theorem, determine x.
9. Which theorem or postulate
2.4a can be used to prove that
these two triangles are
similar?
a. 2 units
b. 6 units
c. 9 units
d. 12 units
a. AA
b. SAS
ABC ∼ DEF . Which of the
7.
2.4a
c. SSA
d. SSS
following is not true?
a.
b.
AB
DE
AB
DE
=
=
EF
BC
AC
DF
c.
AC
BC
=
10. Identify the true statement
2.4a for the figure below.
DF
EF
d. ∠B ≅ ∠E
a.
b.
Moore Public Schools
Geometry EOI Practice
31
PQR ~ RST
PQR ~ TSR
c.
d.
PQR ~ STR
PQR ~ TRS
Geometry EOI Practice
11. If the corresponding sides of
2.4a two triangles are
proportional, then _?_.
13.
2.4a
If ABC ~ PBQ, then
which of the following
proportions is not true?
a. the triangles are congruent
b. the triangles are right
triangles
c. corresponding side lengths
are equal
d. the triangles are similar
a.
b.
PB
AB
AC
PQ
=
PQ
=
CB
AC
QB
c.
d.
AP
PB
AP
PB
=
=
AC
PQ
CQ
QB
12. Shown below is an
2.4a illustration of the _?_.
14. The postulate or theorem
2.4a that can be used to prove
that the two triangles are
similar is _?_.
a. AA Similarity Postulate
b. SAS Similarity Theorem
c. SSS Similarity Theorem
d. SAS Congruence Theorem
a. SSS Similarity Theorem
b. SAS Similarity Theorem
c. AA Similarity Postulate
d. ASA Congruence
Theorem
Moore Public Schools
Geometry EOI Practice
32
Geometry EOI Practice
PASS 2.4b: Use ratios of similar 2-dimensional figures to determine
unknown values, such as angles, side lengths, perimeter or circumference,
and area.
1. Which measure is the height
2.4b of the flagpole in the
diagram?
3. Triangles ABC and DEF are
2.4b
similar. The similarity ratio
of
ABC to
DEF is
5
,
2
AB = 40, BC = 25, and AC = 35.
What is the perimeter of
DEF ?
a. 20 units
b. 40 units
a. 11.2 feet
b. 15 feet
c. 17.5 feet
d. 20 feet
4. Figure ABCDE is similar to
2. The triangles below are
2.4b
c. 60 units
d. 100 units
2.4b
similar. The area of the
figure A ' B ' C ' D ' E '. What is
the length of A ' E '?
larger triangle is 48 in. 2 .
What is the area of the
smaller triangle?
a. 16 in. 2
b. 12 in. 2
Moore Public Schools
Geometry EOI Practice
a. 0.72
b. 2.00
c. 8 in. 2
d. 3 in. 2
33
c. 2.40
d. 3.60
Geometry EOI Practice
5. A surveyor wants to find the
2.4b distance d across a river.
Using the measurements
shown, what is a good
estimate of d, in feet?
a. 30 feet
b. 40 feet
8. Compare the larger circle to
2.4b the smaller circle. Which of
the following correctly list
the ratios of their
circumferences, C, and their
areas, A?
c. 50 feet
d. 60 feet
a. C =
6. A person that is 5 feet tall
2.4b casts a 3.5-foot long shadow.
At the same time a telephone
pole casts a 14-foot shadow.
How tall is the telephone
pole?
c. 17.0 feet
d. 20.0 feet
2.4b
7. Find the height, x, of the
2.4b triangle.
Moore Public Schools
Geometry EOI Practice
28
4
16
7
49
4
16
21
12
Find the
b.
34
441
,A=
7
4
ABC ~ DEF .
a.
c. 50
d. 60
144
7
c. C = , A =
9.
a. 30
b. 40
21
,A=
b. C = , A =
d. C =
a. 9.8 feet
b. 15.5 feet
12
16
9
4
3
area
ABC
area DEF
.
c.
d.
16
3
4
9
Geometry EOI Practice
10. The ratio of side lengths of
ABC to DEF is 3:1. Find the
2.4b
lengths of EF and AC.
13. Find x if
ABC ~ JKL.
2.4b
a. 10
b. 14
a. EF = 3, AC = 3 5
c. 25
d. 29
b. EF = 6, AC = 9 5
c. EF = 6, AC = 3 5
14. If quadrilateral ABCD ~
2.4b quadrilateral EFGH, find x.
d. EF = 6, AC = 21
11. In the diagram,
2.4b
AB
BD
=
AC
CE
.
Find the length of AE.
a. 15
b. 20
a. 7.5
c. 17.5
b. 15
d. 13
c. 25
d. 30
15. The rectangles below are
2.4b similar. Find the value of s.
1
3
12. The ratio of the perimeters
ABC to KLM is 3:5.
2.4b of
Which ratio could not be a
ratio of two corresponding
sides?
a.
b.
1.5
2.5
6
10
Moore Public Schools
Geometry EOI Practice
c. 9:15
a. 2.5
b. 3.0
d. 6:15
35
c. 3.5
d. 4.0
Geometry EOI Practice
PASS 2.5a: Determine and verify the relationships of congruency of
triangles, using algebraic and deductive proofs.
1. Which postulate or theorem
2.5a proves the triangles
congruent?
3. Which set of figures
2.5a demonstrates the ASA
Postulate?
a.
b.
a. SSS
b. ASA
c. SAS
d. AAS
c.
2. Which postulate or theorem
2.5a proves the triangles
congruent?
d.
4. Which set of figures
2.5a demonstrates the AAS
Postulate?
a. SAS
b. AAS
c. SSS
d. ASA
a.
b.
c.
d.
Moore Public Schools
Geometry EOI Practice
36
Geometry EOI Practice
5. If CJW ≅ AGS , m∠A = 50, m∠J = 45,
2.5a and m∠S = 16 x + 5, what is x?
a. 17.5
b. 11.875
7. What are the congruent
2.5a triangles in the diagram?
c. 6
d. 5
a.
b.
6. What reason should be given
2.5a for statement 5 in the proof?
ABC ≅ EBD
ABE ≅ CBD
c.
d.
AEB ≅ CBD
ABE ≅ CDB
8. In the figure below,
2.5a
AC ≅ DF and ∠A ≅ ∠D.
Given: DB is the perpendicular
bisector of AC .
Prove:
ADB ≅ CDB
Statements
1. DB is the perpendicular bisector of AC
2. AB ≅ CB
3. ∠ABD ≅ ∠CBD
4. DB ≅ DB
5. ADB ≅ CDB
Which additional information
would be enough to prove
that ABC ≅ DEF ?
Reasons
a. AB ≅ DE
c. BC ≅ EF
b. AB ≅ BC
d. BC ≅ DE
1. Given
2. Midpoint Theorem
3. ⊥ line; all right ∠ s are ≅
4.Reflexive Property
5. _?_
a. SSS
b. AAS
Moore Public Schools
Geometry EOI Practice
c. ASA
d. SAS
37
Geometry EOI Practice
9. In the figure below, it is
2.5a given that BD ≅ CE. To prove
BCD ≅ CBE by the SSS
Congruence Theorem, what
additional information is
sufficient?
11. In the figure below, it is
2.5a given that AD ≅ AE. To
prove
ADC ≅ AEB by the
ASA Congruence Theorem,
what additional information
is sufficient?
a. ∠A ≅ ∠A
c. AB ≅ AC
a. DC ≅ EB
c. ∠ADC ≅ ∠AEB
b. DC ≅ EB
d. ∠ADC ≅ ∠AEB
b. AB ≅ AC
d. ∠A ≅ ∠A
12. Given ABC ≅ DEF , which
2.5a statement is true?
10. Under the conditions stated
2.5a below, what postulate
implies that GHJ and MHO
are congruent?
OH ≅ JH , ∠O ≅ ∠J
a. ∠A ≅ ∠E
c. BC ≅ EF
b. ∠B ≅ ∠F
d. AC ≅ DE
13. In PQR and KLM ,
2.5a
∠P ≅ ∠K , PQ ≅ KL, and
∠Q ≅ ∠L. Which side is
congruent to RQ ?
a. ASA
c. SSS
b. SAS
d. AAS
Moore Public Schools
Geometry EOI Practice
38
a. KM
c. KL
b. ML
d. cannot be determined
Geometry EOI Practice
14. Which theorem or postulate
2.5a can be used to show
ABC ≅ CDA ?
15. The angle needed to apply
2.5a the SAS postulate is the
a. right angle
b. obtuse angle
c. acute angle
d. included angle
a. HL
b. SSS
Moore Public Schools
Geometry EOI Practice
c. SAS
d. AAS
39
Geometry EOI Practice
PASS 2.5b: Use the relationships of congruency of 2-dimensional figures
to determine unknown values, such as angles, side lengths, perimeter or
circumference, and area.
3. EFGHIJ ≅ KLMNOP. What
2.5b is the length of KL ?
1. Which best describes the
2.5b measure of ∠ABC ?
a. 30˚
b. 110.5˚
c. 108˚
d. 74.5˚
2. Using the congruence
2.5b markings on the figure, what
is x?
a. 2
b. 5
c. 7
d. 12
4. Given ∠X ≅ ∠A and ∠Z ≅ ∠C ,
2.5b find the value of x.
a. 6˚
b. 4˚
c. 15˚
d. 9˚
a. 25
b. 27
Moore Public Schools
Geometry EOI Practice
40
c. 29
d. 30
Geometry EOI Practice
5. In ABCD, AB ≅ CD and BC ≅ AD.
2.5b What is the value of x?
a. 5
c. 7
b. 10
d. 6
7. In the diagram, MN is the
2.5b perpendicular bisector of AD.
What are the values of x and y?
a. x = 2, y = 7
c. x = 8, y = 11
b. x = 8, y = 2
d. x = 2, y = 8
6. AB ≅ CD. Find the length of
2.5b BD.
8. M is the midpoint of LN . Find
2.5b the value of x.
a. 8
c. −4
b. 10
d. 7
a. 19
c. 25
b. 43
d. 50
9. EF bisects ∠DEG. What is
2.5b ∠DEF ?
Moore Public Schools
Geometry EOI Practice
41
a. 28.5°
c. 114°
b. 57°
d. 29.5°
Geometry EOI Practice
10. In the diagram, WX ≅ YZ .
2.5b
13. For what value of x is
2.5b ∠ATK ≅ ∠MJS if
m∠ATK = 5 x + 4 and
m∠MJS = 8 x − 11?
Find the length of XZ.
a. 11
c. 15
b. 2
d. 26
a. 29
c. 10
b. 15
d. 5
14. m∠WOX = 2 x + 1 and
2.5b m∠XOY = 3 x − 9.
Find m∠WOY .
11. In the diagram, AB ≅ DE and
2.5b BC ≅ CD. Find the length of
CE.
a. 11
c. 10
b. 22
d. 16
12. In WXYZ, WZ ≅ XY . What is
2.5b the value of x?
a. 1.6
c. 12
b. 3
d. 4
Moore Public Schools
Geometry EOI Practice
42
a. 10
c. 42
b. 21
d. 52
Geometry EOI Practice
PASS 2.6a: Find angle measures and arc measures related to circles.
5. Find m∠1.
For Exercises 1-4, use the
circle below.
2.6a
a. 170˚
b. 85˚
c. 190˚
d. 95˚
1. Find mBC.
2.6a
a. 55˚
b. 90˚
6. Find m AB.
c. 35˚
d. 110˚
2.6a
2. Find mCD.
2.6a
a. 55˚
b. 90˚
c. 35˚
d. 110˚
a. 110˚
b. 70˚
c. 140˚
d. 220˚
3. Find mCAE.
2.6a
a. 180˚
b. 125˚
c. 145˚
d. 215˚
7. Find m ABC.
2.6a
4. Which statement is not true?
2.6a
a.
b.
c.
d.
m AC = mCD
m AB = mED
m AE = mBC + mCD
mCD = m AE
Moore Public Schools
Geometry EOI Practice
a. 58˚
b. 244˚
43
c. 122˚
d. 29˚
Geometry EOI Practice
8. If mEGF = (6 x + 12)° , find the
value of x.
9. If mLNM = (8 x + 12)° , find the
value of x.
2.6a
2.6a
a. 22
b. 11
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Geometry EOI Practice
c. 16
d. 10
a. 14
b. 16.8
44
c. 28
d. 29
Geometry EOI Practice
PASS 2.6b: Find angle measures and segment lengths using the
relationships among radii, chords, secants, and tangents of a circle.
1. Use the diagram to find the
2.6b value of x. Round to the
nearest hundredth, if
necessary.
4. If an inscribed angle has a
2.6b measure of 100˚, what is the
measure of the intercepted
arc?
a. 100˚
b. 200˚
a. 4
b. 5
c. 50˚
d. 0˚
c. 5.62
d. 5.83
5. Find the value of x.
2.6b
2. Use the diagram to find the
2.6b value of x.
a. 178
b. 356
a. 10
b. 20
c. 22
d. 11
c. 89
d. 182
6. If mLNM = 280°, find the value
2.6b of y.
3. What is m AB ?
2.6b
a. 40
b. 80
a. 10˚
b. 20˚
Moore Public Schools
Geometry EOI Practice
c. 30˚
d. 40˚
45
c. 160
d. 140
Geometry EOI Practice
7. Find the values of a and b.
10. Find the values of x and y.
2.6b
2.6b
a. a = 50, b = 50
b. a = 25, b = 50
c. a = 50, b = 25
d. a = 25, b = 25
a.
b.
c.
d.
8. Find the value of x.
x = 6, y = 84
x = 42, y = 48
x = 42, y = 42
x = 48, y = 42
2.6b
11. Find m∠1 .
2.6b
a. 5
b. 3
c. 8
d. 10
a. 75˚
b. 190˚
c. 95˚
d. 150˚
9. Find the values of x and y.
2.6b
12. Find m∠1 .
2.6b
a. x = 80, y = 75
b. x = 105, y = 100
c. x = 75, y = 80
a. 64˚
b. 32˚
d. x = 100, y = 105
Moore Public Schools
Geometry EOI Practice
46
c. 108˚
d. 54˚
Geometry EOI Practice
13. Find the value of y.
16. Find the value of x.
2.6b
2.6b
a. 10
b. 5
a. 26
b. 77
c. 102
d. 51
17. You are standing 16 feet
2.6b from a circular swimming
pool. The distance from
you to a point of tangency is
25 feet. What is the
approximate diameter of the
pool?
14. Find the value of x.
2.6b
a. 3
b. 4
a. 23 ft
b. 46 ft
c. 5
d. 6
15. Find the value of y.
2.6b
a. 2
b. 3
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Geometry EOI Practice
c. 9.6
d. 14
c. 4
d. 5
47
c. 19 ft
d. 38 ft
Geometry EOI Practice
PASS 3.1: Use the Pythagorean Theorem and its converse to find missing
side lengths and to determine acute, right and obtuse triangles, and verify
using algebraic and deductive proofs.
4. What is the length of the
3.1 hypotenuse of the triangle below to
the nearest tenth?
1. Find the missing length.
3.1
a. 13.23
c. 35
b. 25
d. 625
2. What is the perimeter of
3.1 the nearest tenth?
ABC to
a. 19.8 in.
c.
b. 22.2 in.
d. 20.2 in.
b. acute
d. right
Moore Public Schools
Geometry EOI Practice
b. 8.6 in.
d. 7.6 in.
a. 11 ft
c. 13 ft
b. 12 ft
d. 14 ft
6. What is the perimeter of
3.1 the nearest tenth?
3. If a triangle has sides of 15, 9, and
3.1 20, is it an obtuse, acute,
equilateral, or right triangle?
c. equilateral
c. 8.1 in.
5. A farmer leans a 12-ft ladder
3.1 against a barn. The base of the
ladder is 3 ft from the barn. To the
nearest foot, how high on the barn
does the ladder reach?
9.9 in.
a. obtuse
a. 9.1 in.
48
ABC to
a. 19.8 in.
c. 9.9 in.
b. 22.2 in.
d. 20.2 in.
Geometry EOI Practice
7. What is the perimeter of the figure
3.1 below?
9. A triangle with side lengths of 5,
3.1 12, and 13 is a(an):
a. acute triangle
b. right triangle
c. obtuse triangle
a. 52 units
c. 47.8 units
b. 30 units
d. 49.5 units
d. straight triangle
10. What is the perimeter of the
triangle below? Round the
3.1
answer to the nearest tenth of a
unit.
8. If ABCD is a square and BC = 4
3.1 kilometers, what is BD?
a. 4 2 kilometers
b. 4 kilometers
c. 4 3 kilometers
d. 8 kilometers
a. 9.3 units
b. 12.0 units
c. 20.6 units
d. 86.0 units
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Geometry EOI Practice
PASS 3.2: Apply the 45-45-90 and 30-60-90 right triangle relationships to
solve problems, and verify using algebraic and deductive proofs.
1. Find the value of x.
4. In
3.2
3.2
a. 24 2
c. 12 2
b. 24
d. 12
2. Find the values of x and y.
ABC , what is BC?
a. 4 3
c. 8
b. 4
d. 8 2
5. A triangle whose side lengths
3.2 measure 3, 3, and 3 2 is often
referred to as a(an):
3.2
a. 45-45-90 triangle
b. 30-60-90 triangle
a. x = 15 3; y = 45
c. obtuse triangle
b. x = 15 2; y = 30
d. acute triangle
c. x = 30; y = 45
d. x = 15 3; y = 30
6. What is the length of the
3.2 hypotenuse of a triangle with
vertices of (5, 5), (5, − 4),
and ( − 4, − 4)?
3. What is AC?
3.2
a. 5 2
c. 10 2
b. 20
d. 5 3
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50
a. 18 2
c. 9 2
b. 9 3
d. 81 2
Geometry EOI Practice
7. In order to determine the area
3.2 of a trapezoid, you must
know the height. What is the
height of the trapezoid
shown?
a. 3
b.
5 2
2
c. 5
d. 5 2
8. Find the perimeter of the
3.2 parallelogram. Leave your
answer in simplest radical
form.
a. 13 + 5 2 units
b. 26 + 5 2 units
c. 26 + 10 2 units
d. 26 + 25 2 units
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Geometry EOI Practice
PASS 3.3: Express the trigonometric functions as ratios and use sine,
cosine, and tangent ratios to solve real-world problems.
3. Find x to the nearest hundedth.
1. Choose the correct expression for
tan H.
3.3
3.3
a. x = 24.89
a.
b.
2. In
3.3
GK
KH
GH
KH
c.
d.
b. x = 13.43
GK
GH
c. x = 10.28
KH
d. x = 12.26
KG
4. From a point 125 feet from the
3.3 base of a building, the angle of
elevation from the ground to the
top of the building is 50°.
STU , what is the sine ratio of
∠T ?
a.
b.
9
15
12
15
c.
d.
9
12
What is the height (h) of the
building? Round the answer to the
nearest foot.
15
12
a. 105 feet
b. 149 feet
c. 163 feet
d. 194 feet
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Geometry EOI Practice
5. Using the dimensions of the sail
3.3 given, which most closely
represents sin A?
7. A ship’s anchor rests on the sea
3.3 floor 125 feet below the surface.
The angle of elevation from the
anchor to the ship is 38°. How
long is the anchor chain to the
nearest foot?
a. 77 feet
c. 160 feet
b. 159 feet
d. 203 feet
8. At a certain time, a vertical pole 10
feet tall casts a 14-foot shadow.
What is the angle of elevation of
the sun to the nearest degree?
3.3
a. 0.4706
c. 1.1333
b. 0.8824
d. 1.8750
6. Johnny wants to build a 15-foot
3.3 sloped roof at an angle of 43°, as
shown in the diagram below.
What is the height (h) of the beam
that is needed to support the roof?
Round the answer to the nearest
foot.
a. 10 feet
c. 14 feet
b. 11 feet
d. 22 feet
Moore Public Schools
Geometry EOI Practice
53
a. 36°
c. 46°
b. 44°
d. 54°
Geometry EOI Practice
PASS 4.1a: Identify, describe, and analyze polyhedra (for example,
regular, decahedral).
1. Which of the figures shown is not
4.1a a polyhedron?
a. I only
c. III only
b. II only
d. II and III
4. Use Euler’s Theorem to find the
4.1a number of faces when a polyhedron
has 8 vertices and 12 edges.
a. 4
c. 8
b. 6
d. 10
5. Which is the best description of
4.1a the cross section of the figure
shown?
2. The polyhedron below has how
4.1a many faces (F) and edges (E)?
a. F = 6, E = 18
b. F = 6, E = 24
c. F = 8, E = 18
d. F = 8, E = 24
3. The polyhedron below has how
4.1a many vertices?
a. 14
c. 16
b. 15
d. 17
Moore Public Schools
Geometry EOI Practice
54
a. circle
c. rectangle
b. square
d. oval
Geometry EOI Practice
PASS 4.1b: Use properties of 3-dimensional figures; side lengths,
perimeter or circumference, and area of a face; and volume, lateral area,
and surface area to determine unknown values and correctly identify the
appropriate unit of measure of each.
3. Find the surface area of the regular
4.1b right prism.
1. The best mathematical name of the
4.1b solid is
a. right prism.
a. 215 in.²
c. 105 in.²
b. right rectangular prism.
b. 160 in.²
d. 187.5 in.²
c. cube.
4. Find the surface area of a right
4.1b rectangular prism with a height of
6 inches, a length of 2 inches, and
a width of 8 inches.
d. right pentagonal prism.
2. Find the lateral area of the right
prism shown.
4.1b
a. 96 in.²
c. 152 in.²
b. 120 in.²
d. 128 in.²
5. Find the surface area of the right
4.1b cylinder. Round to the nearest
hundredth.
a. 105 m 2
c. 85 m 2
b. 90 m2
d. 74 m2
Moore Public Schools
Geometry EOI Practice
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a. 831.27 in.²
c. 395.84 in.²
b. 252 in.²
d. 506.68 in.²
Geometry EOI Practice
6. Use the diagram to solve for the
4.1b value of x given that the surface
area of the figure is 286 in.².
a. 14 in.
c. 6 in.
b. 12 in.
d. 7 in.
9. Find the surface area of the cone.
4.1b Round to the nearest tenth.
a. 317.0 m²
c. 239.4 m²
b. 241.7 m²
d. 278.2 m²
10. Use the diagram to solve for x
4.1b and y when the surface area is
138.23 m².
7. Find the slant height of the
4.1b pyramid.
a. 4.5 cm
c. 6.5 cm
a. x = 9.8 m, y = 10 m
b. 5.5 cm
d. 6 cm
b. x = 11 m, y = 10.8 m
c. x = 8 m, y = 7.7 m
8. Find the slant height of the cone.
4.1b Round to the nearest tenth.
d. x = 20 m, y = 19.9 m
11. Find the surface area of the solid.
4.1b The cylinder and cones are right.
Round to the nearest tenth.
a. 716.3 m²
b. 867.1 m²
a. 20.0
c. 8.9
b. 10.6
d. 14.4
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c. 1168.7 m²
d. 942.5 m²
56
Geometry EOI Practice
12. Find the lateral area of the
4.1b pyramid.
16. Find the volume of a prism that
4.1b has a height of 10.5 m and has a
right triangle for a base. The legs
of the triangle are 5 m and 7 m.
Round answer to nearest
hundredth.
a. 57.5 cm²
b. 65 cm²
c. 32.5 cm²
d. 78 cm²
13. What is the volume of a prism
with a rectangular base, with
4.1b
sides of 5 feet and 6 feet, and a
height of 4 feet?
a. 183.75 m 3
c. 367.5 m 3
b. 225.80 m 3
d. 316.14 m 3
17. A cylinder has a radius of 24.6
3
4.1b in. and a volume of 29,468 in. .
Find its height.
a. 60 ft 3
c. 120 ft 3
a. 14.5 in.
c. 15 in.
b. 240 ft 3
d. 180 ft 3
b. 15.5 in.
d. 16 in.
18. Find the value of x if the volume
of the prism is 105 cm 3 .
4.1b
14. Find the value of x if the right
3
4.1b prism has a volume of 24 m .
a. 1 m
a. 2 cm
b. 2 m
b. 3 cm
c. 3 m
c. 4 cm
d. 4 m
d. 5 cm
19. Find the surface area of the
4.1b sphere. Round to the nearest
tenth.
15. Find the volume of the right
4.1b
cylinder. Round the answer to
the nearest hundredth.
a. 324.59 ft 3
a. 175.9 in.²
b. 216.97 ft 3
b. 615.8 in.²
c. 1996.22 ft 3
c. 307.8 in.²
d. 681.64 ft 3
d. 461.8 in.²
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Geometry EOI Practice
20. Find the volume of the sphere.
4.1b Round to the nearest tenth.
a. 44,602.2 m 3
b. 1520.5 m 3
c. 1393.8 m 3
d. 5575.3 m 3
21. What is the radius of a sphere
4.1b with surface area of 1963.5 cm²?
a. 11 cm
c. 11.5 cm
b. 12.5 cm
d. 12 cm
22. Find the circumference of the
great circle if the volume of the
4.1b
sphere is 179.6 m 3 . Round to the
nearest tenth.
a. 22 m
c. 11 m
b. 23.8 m
d. 11.9 m
23. Find the surface area of the
4.1b hemisphere. Round to the
nearest tenth.
a. 706.9 cm²
b. 1413.7 cm²
c. 2120.6 cm²
d. 3534.3 cm²
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Geometry EOI Practice
PASS 4.2a: Use ratios of similar 3-dimensional figures to determine
unknown values such as angles, side lengths, perimeter or circumference
of a face, area of a face, and volume.
4. Which of the following describes
4.2a the two spheres?
1. Two prisms are similar with a
4.2a scale factor of 1:4. Find the
volume of the first given that the
volume of the second is 2400 ft 3 .
a. 600 ft 3
c. 150 ft 3
b. 37.5 ft 3
d. 75 ft 3
c. 1024 m3
b. 640 m3
d. 97.7 m3
c. both A and B
b. similar
d. neither A nor B
5. Two similar prisms have equilateral
4.2a triangular bases and the edges of the
bases are 50 centimeters and 20
centimeters. Find the ratio of the
perimeters of the bases.
2. Two pyramids are similar with a
4.2a ratio of surface areas of 25:64.
Find the volume of the second
pyramid given that the first has a
volume of 250 m3 .
a. 61.0 m3
a. congruent
a. 5 2 : 2 5
c. 25:4
b. 5:2
d. 125:8
6. Two square pyramids are similar.
4.2a The sides of the bases are 4 inches
and 12 inches. The height of the
smaller pyramid is 6 inches. Find
the height of the larger pyramid.
3. Which solid is similar to this
4.2a solid?
a. 24 in.
c. 16 in.
b. 18 in.
d. 14 in.
7. The ratio of the radii of two similar
4.2a cylinders is 3:5. The volume of the
smaller cylinder is 54π cubic
centimeters. Find the volume of the
larger cylinder.
Moore Public Schools
Geometry EOI Practice
59
a. 90π cm3
c. 250π cm3
b. 150π cm3
d. 540π cm3
Geometry EOI Practice
PASS 4.2b: Use the relationships of congruency of 3-dimensional figures to
determine unknown values, such as angles, side lengths, perimeter or
circumference of a face, area of a face, and volume.
3. Cylinders A and B are congruent.
4.2b Cylinder A has a height of 3 inches
and a lateral area of 30π square
inches. What is the surface area of
cylinder B?
1. Two solids are congruent. Which
4.2b statement about the two solids is
true?
a. They have a scale factor of 1.
LA = 2π rh
b. Their corresponding angles are
congruent.
SA = 2π r 2 + 2π rh
c. The ratio of the corresponding
linear measurements is 1:1.
a. 30π square inches
b. 50π square inches
d. All of the above are true
statements.
c. 55π square inches
d. 80π square inches
2. Samantha is making pincushions
4.2b that are congruent rectangular
prisms. The volume of one
pincushion is 96 cubic centimeters,
the height is 2 centimeters, and the
length is 6 centimeters. What is
the width of the other pincushion?
a. 2 centimeters
b. 4 centimeters
c. 6 centimeters
d. 8 centimeters
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Geometry EOI Practice
PASS 4.3: Create a model of a 3-dimensional figure from a 2-dimensional
drawing and make a 2-dimensional representation of a 3-dimensional
object (for example, nets, blueprints, perspective drawings).
1. Which net represents the surfaces
4.3 of a square pyramid?
a.
b.
c.
d.
2. Which of the following patterns
4.3 could not be folded into a cube?
.
.
a.
.
b.
.
c.
.
d.
.
.
.
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Geometry EOI Practice
3. Which could be the view of this
4.3 stack of cubes from directly
above?
a.
b.
c.
d.
4. Which represents a two4.3 dimensional view from directly
above the figure?
.
a.
.
b.
.
c.
.
d.
.
.
.
5. Below are the front, side, and top
4.3 views of a building.
.
How tall (in stories) is the
building?
Moore Public Schools
Geometry EOI Practice
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a. 1
c. 3
b. 2
d. 4
Geometry EOI Practice
6. What figure does the net
4.3 represent?
8. Which is the top view of the farm
4.3 buildings shown above?
a. a right triangular prism
b. a right cylinder
c. a regular cube
a.
.
b.
.
d. a regular triangular pyramid
7. Below are the front, side, and top
4.3 views of a building.
c.
Where is the tallest part of the
building located?
d.
a. front left section
b. back right section
c. back left section
d. front right section
Moore Public Schools
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..
;.
Geometry EOI Practice
PASS 5.1: Use coordinate geometry to find the distance between two
points; the midpoint of a segment; and to calculate the slopes of parallel,
perpendicular, horizontal, and vertical lines.
3. If (2, 2), (8, 2), (8, 8), and (2, 8)
5.1 are the vertices of a square, what
are the slopes of its diagonals?
1. Which equation best
5.1 represents a line parallel to t?
a. 1 and 1
c. 1 and -1
b. 0 and undefined
d. 0 and 0
4. DE has endpoints (-3, 4) and (5, 2).
What is the midpoint of DE ?
5.1
a. y = −2
c. x = 2
b. y = x − 2
d. x = −2
a. (1, 1)
c. (2, 2)
b. (4, 3)
d. (1, 3)
The grid below shows the location of
a high school and a library. A
community center is at the midpoint
between the school and the library.
2. Which equation best
5.1 represents a line parallel to t?
a. y = 2 x − 2
1
b. y = 1 x + 2
2
Moore Public Schools
Geometry EOI Practice
5. What are the coordinates of the
5.1 community center?
c. y = − x − 2
d. y = − x + 2
64
a. (2, 2)
c. (4, 2)
b. (2, 4)
d. (4, 4)
Geometry EOI Practice
7. Tim made a graph of the location of
5.1 some playground equipment as
shown above. What is the distance
between the swings and the slide to
the nearest tenth of a unit?
6. The figure above shows the location
5.1 of two flags on the city’s courthouse
grounds. The state flag will be
located at the midpoint between the
U.S. flag and the city flag. At which
point will the state flag be located?
a. 7.1
⎛ 11 5 ⎞
a. ⎜ − , ⎟
⎝ 2 2⎠
b. 7.6
b. ( −3, 5 )
c. 12.7
( −1, 2 )
d. 13.0
c.
⎛3 1⎞
d. ⎜ , − ⎟
⎝2 2⎠
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Geometry EOI Practice
9. The line in the diagram above
5.1 represents a cable used to support a
newly planted tree. A second cable
is needed that is parallel to the
existing cable. Which could be the
equation of a second cable?
a. y = −2 x + 5
8. What is the midpoint of AB shown
5.1 on the graph above?
1
b. y = − x + 5
2
⎛ 9 ⎞
a. ⎜ − , 3 ⎟
⎝ 2 ⎠
c. y =
d. y = 2 x + 5
⎛3 ⎞
b. ⎜ , 1⎟
⎝2 ⎠
c.
1
x+5
2
( 3, 2 )
10. Find the slope of the line through
5.1
( −5, − 1) and ( −2, − 1) .
⎛9
⎞
d. ⎜ , − 3 ⎟
⎝2
⎠
a. 0
c.
3
4
b. undefined
d.
4
3
11. The slope of a line perpendicular
to the line whose equation is
5.1
y = 3 x − 4 is
Moore Public Schools
Geometry EOI Practice
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a. −
1
3
c. −3
b.
1
3
d. −1
Geometry EOI Practice
12. Find the distance between points
5.1
P (1, − 2 ) and Q ( 0, 2 ) .
a.
15
c.
13
b.
17
d.
5
13. Find the coordinates of the other
endpoint of a segment with an
5.1
endpoint of X (13, 5 ) and
midpoint M ( 8, 3) .
a. (18, 7 )
c. ( 3, 7 )
b. (18, 1)
d. ( 3, 1)
14. Find the coordinates of the other
endpoint of a segment with an
5.1
endpoint of X ( −2, 3) and
midpoint M (1, − 2 ) .
a.
( 4, − 7 )
b. ( −4, 7 )
Moore Public Schools
Geometry EOI Practice
c. ( 0, − 1)
d.
( −5, 8)
67
Geometry EOI Practice
PASS 5.2a: Given a set of points determine the type of figure formed based
on its properties.
1. What is the classification of ABC
5.2a with vertices A(4,1), B(2, -1), and
C(-2, -1) by its sides?
a. equilateral
c. scalene
b. isosceles
d. right
2. What is the classification of ABC
5.2a with vertices A(0, 0), B(4, 3), and
C(4, -3) by its sides?
a. equilateral
c. scalene
b. isosceles
d. right
3. ABCD is a parallelogram with
5.2a A(0, 0), B(2, 4), and C(10, 4). Find
the possible coordinates of D.
a. (8, 0)
c. (0, 4)
b. (10, 0)
d. (10, 8)
4. What is the most precise name for a
5.2a quadrilateral with (2, -1), (6, 3),
(-2, 3), and (2, 9)?
a. rectangle
c. kite
b. parallelogram
d. rhombus
5. What special type of quadrilateral
5.2a has the vertices F(-6, -2), G(1, -2),
H(-6, -5), and I(1, -5)?
a. rectangle
c. square
b. parallelogram
d. rhombus
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Geometry EOI Practice
PASS 5.2b: Use transformations (reflection, rotation, translation) on
geometric figures to solve problems within coordinate geometry.
1. Choose the notation below that
5.2b describes the translation.
3. The coordinates of JKL are
5.2b J(-1, 2), K(-2, -1), and L(2, 1).
The component form of MN is
3, − 4 . What are the coordinates
of J ′K ′L′ after the translation
using MN ?
a. J ′(−4, − 2), K ′(1, − 3), L′(5, − 5)
b. J ′(2, − 2), K ′(1, − 3), L′(5, − 3)
a. ( x, y ) → ( x − 3, y + 4)
c. J ′(2, − 2), K ′(1, − 3), L′(5, − 5)
b. ( x, y ) → ( x − 3, y − 4)
d. J ′(2, − 2), K ′(1, − 5), L′(5, − 3)
c. ( x, y ) → ( x − 4, y + 3)
d. ( x, y ) → ( x − 4, y − 3)
A windmill has eight equally spaced
blades that rotate in the clockwise
direction.
2. Choose the correct name and
5.2b component form of the vector
shown.
a. JH , 3,4
b. JH , −3, −4
c. JH , −4, −3
4. How many degrees must blade P
5.2b rotate to reach the location of
blade U?
d. HJ , 3,4
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a. 45°
c. 225°
b. 135°
d. 300°
Geometry EOI Practice
5. To plan a scene in an animated
5.2b movie, Roger rotates the above
figure around point P by 90° in a
clockwise direction. Which
drawing shows the pre-image and
the final image?
6. Which would move Flag A to Flag B
5.2b in the grpah above?
a.
a. clockwise rotation of 180°
b. reflection over x-axis, then
clockwise rotation of 90°
c. translation 8 units left and 7
units down
b.
d. reflection over y-axis, then
translation 8 units left and 7
units down
c.
d.
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Geometry EOI Practice
7. A quilt design is formed by
5.2b translating a polygon across the
coordinate plane as shown in the
figure above. Which is a
translational rule that will translate
point A to point B?
9. Janelle and Franz are playing a
5.2b game. The rule of the game is each
playing piece must go through one
transformation. Janelle reflects
piece X over line 3. Where will
piece X land?
a. ( x, y ) → ( x + 0, y + 8)
a. on piece A
c. on piece C
b. ( x, y ) → ( x − 4, y + 2)
b. on piece B
d. on piece D
c. ( x, y ) → ( x + 2, y + 3)
d. ( x, y ) → ( x + 4, y − 2)
10. If the point (2, -5) is reflected in
the line y = x, then the image is
5.2b
8. After this translation
5.2b ( x, y ) → ( x + 3, y − 2 ) of point T,
what are the coordinates of the new
point?
a.
( −1, 3)
b. ( 0, 4 )
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Geometry EOI Practice
a. (-5, 2)
c. (-2, 5)
b. (5, -2)
d. (-5, -2)
11. What is the image of (-3, 6) when
reflected in the x-axis?
5.2b
c. ( 3, − 2 )
d. ( 5, − 1)
71
a. (-3, -6)
c. (3, -6)
b. (-3, 6)
d. (3, 6)
Geometry EOI Practice
Answer Key
Pass 1.1
Pass 1.2
Pass 2.2a
Pass 2.2b
1.
d
1.
a
1.
a
1.
d
2.
c
2.
d
2.
b
2.
a
3.
c
3.
c
3.
c
3.
c
4.
d
4.
b
4.
b
4.
b
5.
c
5.
d
5.
c
5.
d
6.
a
6.
a
6.
c
6.
b
7.
c
7.
c
7.
d
7.
d
8.
c
8.
d
8.
b
8.
d
9.
c
9.
c
9.
b
9.
d
10.
b
10.
a
10.
b
10.
d
11.
d
11.
c
11.
d
12.
a
12.
a
13.
c
13.
b
14.
b
Moore Public Schools
Geometry EOI Practice
72
Geometry EOI Practice
Pass2.2c
1.
b
2.
d
1.
d
1.
d
1.
d
3.
d
2.
c
2.
d
2.
c
4.
d
3.
d
3.
c
3.
b
5.
c
4.
c
4.
b
4.
d
6.
b
5.
c
5.
a
5.
a
7.
b
6.
c
6.
a
6.
c
8.
c
7.
a
7.
d
7.
b
9.
c
8.
a
8.
a
8.
c
10.
d
9.
c
9.
d
9.
a
11.
d
10.
d
10.
a
10.
b
12.
c
11.
b
11.
c
11.
b
13.
a
12.
b
12.
d
12.
a
14.
b
13.
a
13.
c
13.
c
15.
c
14.
b
14.
b
14.
b
16.
a
15.
c
15.
d
15.
c
17.
d
16.
a
16.
a
18.
c
17.
b
17.
c
19.
a
18.
c
18.
a
19.
b
19.
d
20.
c
20.
d
21.
b
21.
c
22.
a
22.
c
23.
d
23.
b
24.
a
24.
a
25.
c
26.
a
27.
d
Moore Public Schools
Geometry EOI Practice
Pass 2.3a
Pass 2.3b
73
Pass 2.3c
Geometry EOI Practice
Pass 2.3d
Pass 2.4a
Pass 2.4b
Pass 2.5a
1.
c
1.
c
1.
c
1.
d
2.
a
2.
b
2.
d
2.
b
3.
b
3.
a
3.
b
3.
b
4.
b
4.
c
4.
b
4.
a
5.
d
5.
d
5.
b
5.
d
6.
c
6.
b
6.
d
6.
d
7.
a
7.
c
7.
a
7.
b
8.
a
8.
b
8.
c
8.
a
9.
b
9.
a
9.
a
9.
b
10.
c
10.
c
10.
b
10. a
11.
d
11.
c
11. c
12.
b
12.
d
12. c
13.
c
13.
d
13. b
14.
c
14.
c
14. a
15.
d
15. d
Moore Public Schools
Geometry EOI Practice
74
Geometry EOI Practice
Pass 2.5b
Pass 2.6a
Pass 2.6b
Pass 3.1
1.
b
1.
c
1.
d
1.
b
2.
a
2.
b
2.
c
2.
b
3.
c
3.
d
3.
d
3.
a
4.
c
4.
d
4.
b
4.
d
5.
b
5.
b
5.
c
5.
b
6.
a
6.
c
6.
a
6.
b
7.
d
7.
b
7.
c
7.
c
8.
c
8.
a
8.
d
8.
a
9.
a
9.
d
9.
b
9.
b
10.
d
10.
d
10. c
11.
d
11.
c
12.
d
12.
b
13.
d
13.
d
14.
c
14.
a
15.
b
16.
d
17.
a
Moore Public Schools
Geometry EOI Practice
75
Geometry EOI Practice
Pass 3.2
Pass 3.3
Pass 4.1a
Pass 4.1b
1.
c
1.
a
1.
d
1.
d
2.
d
2.
b
2.
c
2.
b
3.
a
3.
c
3.
c
3.
a
4.
b
4.
b
4.
b
4.
c
5.
a
5.
b
5.
c
5.
d
6.
c
6.
a
6.
d
7.
b
7.
d
7.
c
8.
c
8.
a
8.
d
9.
a
10. d
11. d
12. b
13. c
14. d
15. b
16. a
17. b
18. b
19. d
20. a
21. b
22. a
23. a
Moore Public Schools
Geometry EOI Practice
76
Geometry EOI Practice
Pass 4.2a
Pass 4.2b
Pass 4.3
Pass 5.1
1.
b
1.
d
1.
b
1.
a
2.
c
2.
d
2.
d
2.
b
3.
d
3.
d
3.
c
3.
c
4.
b
4.
b
4.
d
5.
b
5.
b
5.
d
6.
b
6.
d
6.
c
7.
c
7.
c
7.
d
8.
b
8.
b
9.
c
10. a
11. a
12. b
13. d
14. a
Moore Public Schools
Geometry EOI Practice
77
Geometry EOI Practice
Pass 5.2a
Pass 5.2b
1.
c
1.
d
2.
b
2.
b
3.
a
3.
d
4.
c
4.
c
5.
a
5.
c
6.
a
7.
d
8.
d
9.
b
10.
a
11.
a
Moore Public Schools
Geometry EOI Practice
78