Obsolete Geometry Semester 1 Exam Compilation …rpdp.net/admin/images/uploads/resource_8503.docx · Web viewObsolete Geometry Semester 1 Exam Compilation 2008-2011 September 13,2013Page

Obsolete Geometry Semester 1 Exam Compilation 2008-2011

The 2008 to 2012 Geometry and Geometry Honors practice semester exams are no longer available in the CPD Mathematics folder in Interact. However, teachers can use the Geometry Compilation documents for extra practice problems in their daily lesson. These documents are made up of previous years’ practice semester exams and released semester exams. Each objective is made up of four problems that have been compiled from practice exams created in 2008 and the released exams from June of 2009, 2010, and 2011.

These problems are not intended to be used as study guides for this year’s Geometry semester exams as they sometimes do not align to the district’s newly adopted Common Core State Standards for Geometry. Instead, teachers are encouraged to use this resource to provide students with more practice of a specific skill or as a long term memory review tool.

Each set of four problems begins with the district syllabus objective (now obsolete), then is followed by a problem from the 2008 practice test, one problem from the released 2009 semester exam, one problem from the released 2010 semester exam and one problem for the released 2011 semester exam.

In order to identify which year each problem comes from, the number after the dash will specify the origin of that problem. For example, #17 will begin with the syllabus objective in bold letters then will be followed by four problems: (17-8), (17-9), (17-10) and (17-11). The number after the dash indicates the year that problem was created and used. (17-8) is #17 from the 2008 practice test, (17-9) is #17 from the released 2009 semester exam etc.

New Geometry practice problems that align to the CCSS Geometry standards will be posted soon in interact.

September 13,2013 Page 1

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1 23

45

2

1

3 4

5


(1) 1.5 Classify pairs of angles.

(1-8) Use the figure below.

Which best describes the pair of angles: and ?

A. verticalB. adjacent C. linear pair D. complementary


Which best describes the pair of angles and ?

A. AdjacentB. ComplementaryC. linear pairD. vertical

(1-10) Use the diagram.


A. complementaryB. linear pairC. supplementaryD. vertical



341

25

12

4

3

A

D

EF

CB

12

4

3

A

D

E

CB

F



A. complementaryB. linear pairC. supplementaryD. vertical

(2) 1.5 Classify pairs of angles.

(2-8) In the diagram below, , , and are right angles.


A. verticalB. adjacentC. supplementary D. complementary

(2-9) Use the diagram below.


A. adjacentB. complementaryC. linear pair D. right


12

43A

E

CB

F

D

5

A

E

CB

F

D




A. verticalB. supplementaryC. linear pairD. adjacent



A. adjacentB. linear pairC. supplementaryD. vertical


B

A

D

C

7 2x 3x

B

A

D

C

4 3x 3x


(3) 1.6 Solve segment and angle problems using algebraic techniques.

(3-8) In the diagram below, .

What is the value of x?

A. 2

B.C. 4

D.

(3-9) In the diagram below, .


A.

B. 7

C. 10

D.


B

A

D

C

5 12x 3x

P 2 10x 2x

N

L

M


(3-10) In the diagram, .


A. 3

B. 4

C. 6

D. 7



A. 27

B. 22

C. 16

D. 11


Z

3a + 8 a

YX

Z

a + 9 2a

YX

Z

6a – 5 4a

YX


(4) 1.6 Solve segment and angle problems using algebraic techniques.

(4-8) In the figure below, Y is between X and Z and cm.

What is the value of a?

A. 4

B. 8

C. 12

D. 16

(4-9) In the figure below, Y is between X and Z, and .


A. 7

B. 9

C. 13

D. 19

(4-10) In the diagram, Y is between X and Z, and .

What is the length of ?

A. 5 cm

B. 10 cm

C. 20 cm

D. 25 cm


ZY4b b + 6

X


(4-11) In the diagram, Y is between X and Z,and centimeters.


A. 24 cm

B. 12 cm

C. 10 cm

D. 8 cm

(5) 1.8 Find the distance between two points.

(5-8) What is the distance between points and ?

A. 3

B.

C. 9

D.


A.

B.

C. 4

D. 8


A. 5

B. 25



C.

D.


A.

B.

C. 10

D.

(6) 1.9 Find the midpoint of a segment.

(6-8) What are the coordinates of the midpoint of the segment joining the points A

and B ?

A.

B.

C.

D.

(6-9) What are the coordinates of the midpoint of the segment joining the points

and ?

A.

B.



C.

D.

(6-10) What are the coordinates of the midpoint of the segment joining the points

and ?

A.

B.

C.

D.

(6-11) What are the coordinates of the midpoint of with endpoints and

?

A.

B.

C.

D.

(7) 2.2 Justify conjectures and solve problems using inductive reasoning.

(7-8) In the pattern below, the sides of each regular hexagon have a length of 1 unit.


Figure 1Figure 2Figure 3



What is the perimeter of the figure?

A. 18 units

B. 22 units

C. 26 units

D. 30 units

(7-9) In the pattern below, the sides of each square have a length of 1 unit.


A. nB. 2nC. 2n + 2D. 4n + 4

(7-10) In the pattern, the sides of each regular octagon have a length of 1 unit.


A. 26B. 56C. 62D. 71

(7-11) In the pattern, the sides of each square have a length of 1 unit.




What is the perimeter of the 6th figure?

A. 24B. 30C. 34D. 44

(8) 2.3 Differentiate between deductive and inductive reasoning.

(8-8) In the scientific method, after one makes a conjecture, one tests the conjecture. What type of reasoning is used?

A. conclusiveB. deductiveC. inductiveD. scientific

(8-9) Using the scientific method, conjectures are made based on observed patterns. What type of reasoning does the scientific method use?

A. deductiveB. hypotheticalC. inductiveD. scientific

(8-10) Maria made a conjecture about her next test score based on the pattern of her previous test scores. What type of reasoning did she use?

A. conclusiveB. deductiveC. hypotheticalD. inductive

(8-11) The lawyer presented all the facts of the case in a logical order to the judge. What type of reasoning did the lawyer use?

A. conjectureB. deductiveC. inductiveD. intuitive



(9) 2.6 Analyze conditional or bi-conditional statements.

(9-8) All donks are widgets. Which statement can be written using the rules of logic?

A. A donk is a widget if and only if it is an object.B. An object is a donk if and only if it is a widget.C. If an object is a widget, then it is a donk.D. If an object is a donk, then it is a widget.

(9-9) Which can be written as a bi-conditional statement?

A. All donks are widgets.B. All widgets are prings.C. All donks and all widgets are prings.D. All donks are widgets and all widgets are donks.

(9-10) Jessica made the statement, “If I get a job, then I can pay for a car.” Her friend commented, “If you do not get a job, then you cannot pay for a car.” What type of statement did her friend conclude?

A. biconditionalB. contrapositiveC. converseD. inverse

(9-11) The teacher said, “If all the sides of a triangle are congruent, then it is an equilateral triangle.” A student replied, “If it is not an equilateral triangle, then all the sides are not congruent.” What type of statement did the student use?

A. biconditionalB. contrapositiveC. converseD. inverse

(10) 2.7 Write and analyze the converse, inverse, and contrapositive of a statement.

(10-8) Which statement is the inverse of: If x = 5, then x > 3?



A. If , then .B. If , then .C. If , then .D. If , then .

(10-9) Which statement is the converse ofIf x = 5, then x > 3?


(10-10) What is the contrapositive of the statement?If x = 5, then x > 3.


(10-11) What is the inverse of this statement?If I am in my room, then I am happy.

A. I am in my room, if and only if I am happy.B. If I am happy, then I am in my room.C. If I am not happy, then I am not in my room.D. If I am not in my room, then I am not happy.

(11) 2.7 Write and analyze the converse, inverse, and contrapositive of a statement.

(11-8) Which is a valid counterexample of the converse of the statement: If Hedley lives in North Las Vegas, then he lives in Nevada?

A. Hedley lives in Phoenix.B. Hedley lives in California.C. Hedley lives in Reno.D. Hedley lives in the United States.

(11-9) Which is the inverse of the statement: If Jon lives in North Las Vegas, then he lives in Nevada?



A. If Jon lives in Nevada, then he lives in North Las Vegas.B. If Jon lives in North Las Vegas, then he does not live in Nevada.C. If Jon does not live in Nevada, then he does not live in North Las Vegas.D. If Jon does not live in North Las Vegas, then he does not live in Nevada.

(11-10) What is the converse of the statement?If Sandra passes Geometry, then her father will buy her a new car.

A. If Sandra’s father buys her a new car, then she passed Geometry.B. If Sandra does not pass Geometry, then she will not get a new car.C. If Sandra’s father does not buy her a new car, then she did not pass Geometry.D. If Sandra gets a new car, then she passed Geometry.

(11-11) What is the converse of the statement?If Grandpa lives in California, then he lives in the United States.

A. If Grandpa lives in the United States, then he lives in California.B. Grandpa lives in California, if and only if he lives in the United States.C. If Grandpa does not live in California, then he does not live in the United States.D. If Grandpa does not live in the United States, then he does not live in California.

(12) 2.9 Find counterexamples to disprove mathematical statements.

(12-8) Which is the contrapositive to the statement: If n is odd, then is even.

A. If is odd, then n is even.B. If is even, then n is odd.C. If n is even, then is odd.D. If n is even, then is even.

(12-9) Which is a counterexample to the statement: All prime numbers are odd?

A. 8 is even. B. 7 is prime.C. 5 is odd.D. 2 is prime.

(12-10) Which is a counterexample to the statement?The product of two fractions is never an integer.

A.

B.


m

2

1


C.

D.

(12-11) Which is a counterexample to the statement?All planets have moons.

A. The planet Jupiter has many moons.B. The planet Mars has two moons.C. The planet Mercury has no moons.D. The planet Saturn has many moons.

(13) 3.2 Analyze relationships when two lines are cut by a transversal.(13-8) In the figure below, line m is a transversal.


A. alternate exteriorB. alternate interiorC. correspondingD. vertical

(13-9) In the figure below line m is a transversal.


m

2

1

m

2 1

3 4

m

4132

8576


Which best describes the pair of angles and ?A. alternate exteriorB. alternate interiorC. correspondingD. vertical

(13-10) In the diagram, line m is a transversal.

Which best describes the pair of angles and ?A. alternate exteriorB. alternate interiorC. correspondingD. supplementary

(13-11) In the diagram, line m is a transversal.

Which best describes the angle pair and ?

A. supplementaryB. correspondingC. alternate interiorD. alternate exterior

(14) 3.3 Solve problems which involve parallel or perpendicular lines using algebraic techniques.


64°

n

m

l

4 16x

63°

n

m

l

3 15x

134°

nm

t

2 10x


(14-8) In the figure below, and l is a transversal.

What is the value of x?A. 33B. 29C. 20D. 16



(14-10) In the diagram, and t is a transversal.



n

40°

m

t

2 20x

x°

n

m

l

117°

114°

n

m

l

x°


(14-11) In the diagram, and t is a transversal.






What is the value of x?A. 24


75°

n

ms

y°

m

p

80°

n

x°

q

lF

2 17x

mG

H

65°


B. 66C. 86D. 114

(15-10) In the diagram, and s is a transversal.

What is the value of y?A. 75B. 105C. 125D. 150

(15-11) In the diagram, and .



(16-8) In the figure below, .

What value of x would make line l parallel to line m?A. 41B. 49


lF

5x m

G

H

85°

n

F

20x

mG

H70°

m

40°

t

4y

n


C. 65D. 66


What value of x would make line l parallel to line m?A. 85B. 90C. 95D. 100


What value of x would make line n parallel to line m?A. 40B. 70C. 90D. 130


What value of y would show that line m was parallel to line n?A. 50B. 40C. 35D. 10

(17) 3.4 Write proofs relating to parallel and perpendicular lines.


l

m

1 5

2

3

4

6

7

8

l

m

1 5

2

3

4

6

7

8

s

r

15

23 4

67 8


(17-8) In the figure below, lines l and m are parallel.

Which statement is true?A. and are congruent.B. and are supplementary.C. and are supplementary.D. and are congruent.

(17-9) In the figure below, lines l and m are parallel.

Which statement is true?A. and are supplementaryB. and are supplementaryC. and are congruentD. and are congruent

(17-10) In the diagram, lines r and s are parallel.

Which statement is always true?A. and are congruentB. and are congruent


sr

1

5

2 3 4

678

m

n


C. and are supplementaryD. and are supplementary

(17-11) In order for lines m and n to be parallel, what statement must be true?

A. and are correspondingB. and are complementaryC. and are congruentD. and are supplementary

(18) 4.1 Classify triangles by sides and/or angles.

(18-8) Which is a valid classification for a triangle?A. Acute rightB. Isosceles scaleneC. Isosceles rightD. Obtuse equiangular

(18-9) Which is a valid classification for a triangle?A. Acute rightB. Obtuse equilateralC. Isosceles scaleneD. Isosceles obtuse

(18-10) Which is a valid classification for a triangle?A. equilateral scaleneB. isosceles scaleneC. obtuse isoscelesD. right acute

(18-11) Which is a valid classification of a triangle?A. acute equilateralB. obtuse equiangularC. right acuteD. scalene isosceles


3 3x 45°

x°

3 10x 70°

x°

4 25x x°

80 °


(19) 5.6 Solve problems involving properties of polygons.

(19-8) Use the triangle below.


(19-9) Use the triangle below.


(19-10) Use the triangle.



6x

85° 5 5x

7 10x


(19-11) Use the quadrilateral.


(20) 4.3 Analyze the relationships between congruent figures.

(20-8) In the figures below, .


W

V

U

T

S

R B

A

F

E

D

C

A

E

D C

B

V

U

T S

R


Which side of RSTUVW corresponds to ?

A.

B.

C.

D.


Which side of RSTUV corresponds to ?

A.

B.

C.

D.


E

C

B

A

D

T

SR

U

V

S

R

V

TU

ML

N

J

K



Which side of ABCDE corresponds to ?

A.

B.C.D.


Which angle corresponds to ?A.B.C.D.



(21) 4.6 Prove that two triangles are congruent.(21-8) Use the triangles below.

Which congruence postulate or theorem would prove that these two triangles are congruent?

A. angle-angle-side B. angle-side-angleC. side-angle-side D. side-side-side

(21-9) Use the triangles below.

Which congruence postulate or theorem would prove these two triangles are congruent?

A. angle-angle-angleB. angle-side-angleC. side-angle-sideD. side-side-side

(21-10) Use the triangles.

Which congruence postulate or theorem proves these two triangles are congruent?A. angle-angle-angle (AAA)B. angle-side-angle (ASA)C. side-angle-side (SAS)


E

C

D

A

B

E

C

D

A

B


D. side-side-side (SSS)

(21-11) Use the triangles.

Which congruence postulate or theorem proves these two triangles are congruent?A. angle-angle-side (AAS)B. side-angle-side (SAS)C. side-side-angle (SSA)D. side-side-side (SSS)

(22) 4.6 Prove that two triangles are congruent.

(22-8) In the diagram below, and .

Which congruence postulate or theorem would prove that these two triangles are congruent?

A. side-side-sideB. angle-angle-angle C. side-angle-sideD. angle-side-angle

(22-9) In the diagram below, and bisect each other at E.

Which congruence postulate or theorem would prove these two triangles are congruent?A. angle-angle-angleB. angle-side-angleC. side-angle-side


C

D

A B

MK

N

1 2

L


D. side-side-side

(22-10) In the diagram, and B is the midpoint of .

Which congruence postulates or theorems would prove these two triangles are congruent?I. side-side-angle (SSA)

II. side-angle-side (SAS)III. side-side-side (SSS)

A. II onlyB. III onlyC. I and II onlyD. II and III only

(22-11) In the diagram, and .

Which congruence postulate or theorem would prove ?A. angle-side-angle (ASA)B. side-angle-side (SAS)C. side-side-angle (SSA)D. side-side-side (SSS)

(23) 4.5 Solve problems related to congruent triangles using algebraic techniques.

(23-8) Given that , , , and , what is the value of n?

A.

B. 5

C.



D.

(23-9) Given that , , , and , what is the value of a?

A. 2

B. 8

C. 13

D. 15

(23-10) Given that , , , and , what is the value of b?

A.

B. 25

C.

D. 95

(23-11) Given that , , , , and , what is the value of z?

A.

B.

C.

D. 2


(24-8) Given that , , , , and , what is the value of x?

A.

B. 6



C.

D. 19

(24-9) Given that , , , , and , what is the value of x?

A.

B.

C. 15

D. 20

(24-10) Given that , , , , and ; what is the value of x?

A. –1

B. 1

C. 3

D. 6

(24-11) Given that , , , and . What is the value of n?

A.

B.

C. 15

D. 18


C

DA

B X

Y

C

DA

B X

Y


(25) 4.6 Prove that two triangles are congruent.

(25-8) The statements for a proof are given below.

Given: Parallelogram ABCD

Prove:

Proof:STATEMENTS REASONS1. Parallelogram ABCD

1. Given

2. 2.

3. 3.

4. 4.

5. 5.

What is the reason that the statement in Step 4 is true?

A. side-angle-sideB. angle-side-angleC. Opposite sides of a parallelogram are

congruent.D. Corresponding angles of congruent

triangles are congruent.



Prove:


1. Given

2. 2.

3. 3.

4. 4.

5. 5.

What reason makes the statement in Step 4 true?

A. Side-angle-side congruence theorem.B. Angle-side-angle congruence

theorem.C. Opposite sides of a parallelogram are

congruent.D. Corresponding parts of congruent

triangles are congruent.


C

DA

B X

Y

N P

O

M




Prove:


1.

2. 2.

3. 3.

4. 4.

5. 5.


A. angle-angle-side (AAS)B. angle-side-angle (ASA)C. side-angle-side (SAS)D. side-side-side (SSS)


Given:

Prove:

Proof:STATEMENTS REASONS

1. , 1. Given

2. 2.

3. 3.

4. 4.

5. 5.


A. side-angle-side (SAS)B. side-side-side (SSS)C. corresponding parts of congruent

triangles are congruent (CPCTC)D. angle-side-angle (ASA)


C

D

A

B

F

E


(26) 4.4 Justify congruence using corresponding parts of congruent triangles.


Given:

Prove:

Proof:STATEMENTS REASONS

1. 1. Given

2. 2. Given

3. 3. Given

4. 4. ______

5.

5. Corresponding Parts of Congruent Triangles are Congruent

What is the missing reason that would complete this proof?

A. side-side-side

B. side-angle-side

C. angle-side-angle

D. angle-angle-side


C

D

A

B

F

E



Given:

Prove:

Proof:

STATEMENTS REASONS

1. 1. Given

2. 2. Given

3. 3. Given

4. 4. ______

5. 5. ______


A. Angle-angle-side congruence theorem.

B. Angle-side-angle congruence theorem.

C. Definition of congruent segments.

D. Corresponding parts of congruent triangles are congruent.


C

D

A

B

F

E



Given:

Prove:

Proof:

STATEMENTS REASONS

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.


A. corresponding parts of congruent triangles are congruent. (CPCTC)

B. angle-side-angle (ASA)

C. side-angle-angle (SAA)

D. given


K

G

H

J

I



Given: I is the midpoint of

Prove:

Proof:

STATEMENTS REASONS

1. I is the midpoint of

1. Given

2. 2.

3. 3.

4. 4.

5. 5.

What is the reason for the 5th statement?

A. definition of a midpoint

B. angle-side-angle (ASA)

C. prove

D. corresponding parts of congruent triangles are congruent. (CPCTC)




(27-8) Given that , , , and , what is LN?

A. 16

B. 21

C. 57

D. 67

(27-9) Given that , , , and , what is LN?

A. 28

B. 34

C. 101

D. 105

(27-10) Given that , , , and

; what is LN?

A. 15

B. 20

C. 65

D. 75

(27-11) Given that , , , and

, what is the value of x?

A. 1

B. 2

C. 6

D. 15

(28) 4.7 Prove and use the properties of isosceles and/or equilateral triangles.

(28-8) In the isosceles triangle below, .


F

H

G137°

H

G

124°

F

G

130°

F

H


What is the measure of ?

A. 21.5°

B. 26.5°

C. 43°

D. 53°

(28-9) In the isosceles triangle below, .


A. 28°

B. 56°

C. 124°

D. 180°

(28-10) In the isosceles triangle, .


A. 25°

B. 35°

C. 50°

D. 65°

(28-11) In triangle PQR, and .


R

P

Q

7 miles

9 miles

EulerEuclid

Geometria

5 miles

10 miles

RichmondEnterprise

Springfield



A. 27°

B. 54°

C. 63°

D. 117°

(29) 4.11 Solve problems applying the properties of triangle inequalities.

(29-8) Three towns form a triangle on the map below.

Which statement does NOT represent possible distances between Euclid and Geometria?A. Between 2 and 7 miles apart.B. Between 7 and 9 miles apart.C. Between 9 and 16 miles apart.D. Between 49 and 81 miles apart.

(29-9) Three towns form a triangle on the map below.

Which statement represents the possible distance from Enterprise to Springfield?A. Between 1 and 5 miles apart.B. Between 5 and 15 miles apart.C. Between 15 and 30 miles apart.D. Between 30 and 50 miles apart.

(29-10) Three towns form a triangle on the map.


6 miles 10 miles

LeibnizEuler

Newton

18 miles34 miles

WashingtonAlta

Jasper

x


Which inequality represents all possible distances d from Euler to Leibniz?

A. 3 < d < 5

B. 4 < d < 16

C. 6 < d < 10

D. 12 < d < 20

(29-11) Three towns form a triangle on the map.

Which value of x is NOT a possible distance between Alta and Washington?

A. 10 miles

B. 20 miles

C. 30 miles

D. 40 miles


(30-8) The is constructed with vertices , , and . What is

the length of ?

A.

B.

C.D.

(30-9) When is constructed with vertices , , and , what is

the length of ?

A.

B.



C.

D.

(30-10) is constructed with vertices , , and . What is

the length of ?

A.

B.

C.

D.

(30-11) Given and . What is the distance from A to B?

A.

B.

C.

D.


(31-8) In , is a right angle and . Which list shows the sides in order from longest to shortest?

A.

B.

C.

D.

(31-9) In , is a right angle and . Which list shows the sides in order from shortest to longest?



A. , ,

B. , ,

C. , ,

D. , ,

(31-10) In , the and . Which list shows the sides in order from shortest to longest?

A.

B.

C.

D.

(31-11) In , AB = 6 centimeters, BC = 9 centimeters, and CA = 5 centimeters. Which list shows the angles in order from largest to smallest?

A.

B.

C.

D.


(32-8) A triangle has two sides that have lengths of 7 cm and 17 cm. Which could represent the length of the third side of the triangle?

A. 24 cm

B. 18 cm

C. 10 cm

D. 7 cm


14

y

x

11

9z


(32-9) A triangle has two sides that have lengths of 4 cm and 14 cm. Which could represent the length of the third side of the triangle?

A. 3 cm

B. 10 cm

C. 17 cm

D. 18 cm

(32-10) Which list of three lengths would form a triangle?

A. 1, 1, 1

B. 2, 4, 7

C. 3, 4, 11

D. 5, 5, 10

(32-11) Which list of three lengths would form a triangle?

A. 4, 4, 7

B. 4, 5, 10

C. 5, 6, 12

D. 6, 6, 12

(33) 4.13 Apply special segment properties to solve problems.

(33-8) The triangle below contains three midsegments.

What are the values of x, y, and z?

A. x = 9, y = 22, z = 7

B. x = 9, y = 11, z = 14

C. x = 9, y = 22, z = 14

D. x = 18, y = 11, z = 7


7

16

6

x y

z

6

10

8

A

E

B


(33-9) The triangle below contains three midsegments.

What are the values of x, y, and z?

A. x = 8, y = 12, z = 7

B. x = 8, y = 12, z = 14

C. x = 13, y = 9, z = 10

D. x = 12, y = 14, z = 8

(33-10) is a median of .


A. 6

B. 8

C. 10

D. 12

(33-11) is a median of .


C

710

8

A

E

B

C

12

5

S

B

Q

CRD



A. 6

B. 8

C. 10

D. 14

(34) 4.13 Apply special segment properties to solve problems.

(34-8) In , is a midsegment, and .


A. 34

B. 26

C. 17


4

3

G

E

J

FHI

12 cm

5 cm E

B

C

D

A


D. 13

(34-9) In , is a midsegment.


A. 6

B. 8

C. 10

D. 12

(34-10) is a right triangle with AB = 5 cm and BC = 12 cm.

What is the length of midsegment ?A. 2.5 cmB. 6 cmC. 6.5 cmD. 13 cm

(34-11) In , , , and are midsegments, GJ = 6 centimeters, and EI = 8 centimeters.


G

8 cm

6 cm

J

FI

E

H

m

n

l


What is the length of ?A. 10 cmB. 14 cmC. 16 cmD. 20 cm

(35) 4.14 Explore the points of concurrency and their special relationships.

(35-8) The triangle below shows a point of concurrency. Lines l, m, and n, are perpendicular bisectors of the triangle’s sides.

What is the name of the point of concurrency in the triangle?A. centroidB. incenterC. orthocenterD. circumcenter

(35-9) The triangle below shows a point of concurrency. The interior segments are angle bisectors.

What is the name of the point of concurrency in the triangle?A. centroidB. circumcenterC. incenterD. orthocenter

(35-10) The triangle shows a point of concurrency. The interior segments are medians.



What is the name of the point of concurrency in the triangle?A. centroidB. circumcenterC. incenterD. orthocenter


What is the name of the point of concurrency in this triangle?A. centroidB. circumcenterC. incenterD. orthocenter

(36) 5.1 Differentiate among polygons by their attributes.

(36-8) How many sides does a nonagon have?

A. 7

B. 9

C. 11

D. 19

(36-9) How many sides does a heptagon have?

A. 6



B. 7

C. 16

D. 17

(36-10) How many sides does a dodecagon have?

A. 6

B. 10

C. 12

D. 20

(36-11) How many sides does a decagon have?

A. 6

B. 8

C. 10

D. 12

(37) 5.1 Differentiate among polygons by their attributes.

(37-8) Which figure is a polygon?

A.

B.



C.

D.

(37-9) Which figure is a polygon?

A.

B.

C.

D.

(37-10) Which group of figures are all polygons?

A.

B.



C.

D.

(37-11) Which group of figures are all polygons?

A.

B.

C.

D.

(38) 5.3 Find the sum of the measures of the interior angles of a polygon.

(38-8) A hexagon is shown below.


a°

100°

150°

a°

110°

100°



A. 90

B. 100

C. 130

D. 150

(38-9) A pentagon is shown below.


A. 100

B. 110

C. 120

D. 150

(38-10) What is the sum of the measures of the interior angles of a decagon?

A. 1440

B. 1800

C. 2160

D. 2880

(38-11) What is the sum of the measures of the interior angles of this polygon?


x°

60°

40°

130°

x°

150°130°

100°


A. 360

B. 540

C. 720

D. 1080




A. 70

B. 60

C. 50

D. 40

(39-9) The figure below is a hexagon with an external angle.


A. 20

B. 60

C. 80

D. 160


C

B

D

A

31

11x + 9

C

B

D

A 10x – 4

4x + 8

26


(39-10) Given that the exterior angle of a regular polygon is 36°, determine the number of sides of the polygon.

A. 5

B. 10

C. 18

D. 36

(39-11) What is the sum of the exterior angles of a polygon?

A. 180

B. 360

C. 540

D. 720

(40) 5.4 Solve problems involving properties of special quadrilaterals.

(40-8) Parallelogram ABCD is given below.


(40-9) Rectangle ABCD is given below.

What is the value of x?A. 2B. 3

C.

D.


6(x + 4)

25º

B

D C

A

5x + 45

7x + 15


(40-10) Figure ABCD is a rhombus.

What is ?

A. 25

B. 50

C. 65

D. 75

(40-11) The figure below is a rhombus.


A. 2.5

B. 10

C. 15

D. 30

(41) 5.8 Find the measures of interior, exterior, and central angles of a given regular polygon.

(41-8) What is the measure of each exterior angle of a regular hexagon?

A. 60°

B. 90°

C. 120°

D. 135°



(41-9) What is the measure of each exterior angle of a regular octagon?

A. 144°

B. 135°

C. 45°

D. 36°

(41-10) What is the measure of each exterior angle of a regular pentagon?

A. 45°

B. 72°

C. 108°

D. 120°

(41-11) What is the measure of each exterior angle of a regular decagon?

A. 36°

B. 45°

C. 135°

D. 144°


(42-8) Which statement is true about a kite?

A. A kite has 4 congruent sides.

B. A kite has 2 pairs of parallel sides.

C. A kite has perpendicular diagonals.

D. A kite has congruent diagonals.

(42-9) Which statement is true about a trapezoid?

A. A trapezoid has 1 acute angle and 3 obtuse angles.

B. A trapezoid has 2 pairs of parallel sides and 4 sides.

C. A trapezoid has 4 right angles and 2 pairs of parallel sides.

D. A trapezoid has 4 sides and exactly 1 pair of parallel sides.



(42-10) Which statement is true?

A. All rhombi have congruent diagonals.

B. All rhombi have only one pair of parallel sides.

C. All rhombi have perpendicular diagonals.

D. All rhombi have right angles.

(42-11) Which statement is true?

A. All parallelograms have only one pair of parallel sides.

B. All parallelograms have complimentary consecutive angles.

C. All parallelograms have diagonals that bisect each other.

D. All parallelograms have four congruent sides.


(43-8) Which statement below is true about an isosceles trapezoid?

A. Both pairs of opposite sides are parallel.

B. Both pairs of opposite sides are congruent.

C. One pair of opposite sides is congruent and the other is parallel.

D. One pair of opposite sides is both parallel and congruent.

(43-9) Which statement below is true?

A. All rhombi are squares.

B. All squares are rectangles.

C. All quadrilaterals are parallelograms.

D. All rectangles are rhombi.

(43-10) Which statement is true about all rectangles?

A. Adjacent sides are not congruent.

B. Diagonals are perpendicular.

C. They are trapezoids.

D. They are equiangular.


MK

L

8 cm

10 cm47°

B

C

A

53°

CA

B

4 cm

5 cm45°

Z

Y

X

80°


(43-11) Which statement is true about all isosceles trapezoids?

A. Both pairs of opposite sides are congruent.

B. Both pairs of opposite sides are parallel.

C. One pair of opposite sides is both parallel and congruent.

D. One pair of opposite sides is parallel, and the other pair is congruent.

(44) 4.4 Justify congruence using corresponding parts of congruent triangles.


Which statement must be true?

A.

B.

C.

D.



A.

B.

C.

D.


CA

B

5 cm

30°

100°

7 cm

Z

Y

100°

30°

X

B

8cm

C

X

A

10 cm

Z

Y

120°

40°




A.

B.

C.

D.

(44-11) In the diagram, . Which statement must be true?

A.

B.

C.

D.


AB

DC

E

65°

J I

G H

x°

10x

J

G(2x)°

15x I

H


(45) 5.6 Solve problems involving properties of polygons.(45-8) Use the rhombus below.

What is ?A. 25°B. 65°C. 90°D. 115°

(45-9) In trapezoid GHIJ below, .


(45-10) Figure GHIJ is a parallelogram.

What is the value of x?A. 15


J I

G

2 25x

35x

H


B. 40C. 55D. 65

(45-11) Figure GHIJ is a parallelogram.


A. 10

B. 40

C. 60

D. 80

(46) 5.8 Find the measures of interior, exterior, and central angles of a given regular polygon.

(46-8) A regular polygon has interior angles that measure 144°. How many sides does this polygon have?

A. 6

B. 8

C. 10

D. 12

(46-9) A regular polygon has interior angles that measure . How many sides does this polygon have?

A. 30

B. 15

C. 12

D. 10


A. 3


75°

x°41°


B. 6

C. 12

D. 24


A. 4

B. 6

C. 8

D. 10




A. 64

B. 74

C. 116

D. 126



86°123°

x°

65°

120°

x°

70°

56°

93°

91°

x°



A. 23B. 37C. 43D. 57



A. 65

B. 105

C. 110

D. 115



A. 120



B. 128

C. 180

D. 240


(48-8) Given that is an isosceles right triangle, what is the measure of an acute angle of the triangle?

A. 45°

B. 60°

C. 90°

D. 120°

(48-9) Given that is an equilateral triangle, what is ?

A. 30°

B. 45°

C. 60°

D. 90°

(48-10) Given isosceles , where is an obtuse angle, which could be the ?

A. 22°

B. 55°

C. 88°

D. 111°

(48-11) Given that is an equilateral triangle, what is the measure of an acute angle of the triangle?

A. 45°

B. 60°

C. 90°

D. 120°


(49-8) What is the term of the sequence 1, 4, 9, 16, 25 …?


1 2 3 4 … n1 5 9 13 … ?


A.

B.

C.

D.

(49-9) What is the term of the sequence 1, 4, 7, 10, …?

A.

B.

C.

D.

(49-10) Use the table.

What is the nth term of the sequence?

A.

B.

C.

D.

(49-11) Using the table, what is the nth term of the sequence?

1 2 3 4 … n

4 8 12 16 … ?

A.

B.

C.

D.




(50-8) Geometric figures are displayed on a computer screen in the following order: triangle, concave quadrilateral, convex pentagon, concave hexagon. Using inductive reasoning, what prediction can be made about the next figure?

A. It will be a concave heptagon.

B. It will be a convex heptagon.

C. It will be a convex polygon, but the type cannot be predicted.

D. It will be a polygon, but no other details about it can be predicted.

(50-9) On the way to the park, Colin passes 5 dogs that are all black with white spots. Using inductive reasoning, what prediction can he make about the next dog that he passes?

A. The dog will have four legs.

B. The dog’s name will be Spot.

C. The dog will be white with black spots.

D. The dog will be black with white spots.

(50-10) Tina has a peanut butter sandwich for lunch on Monday. She has a peanut butter sandwich for lunch on Tuesday, and the same on Wednesday. Using inductive reasoning, predict the type of sandwich she will have on Thursday.

A. roast beef

B. peanut butter

C. ham and cheese

D. She will not have a sandwich on Thursday.

(50-11) Austin went to track practice after school on Monday, Tuesday, and Wednesday. Using inductive reasoning, what conclusion can you make about his Thursday after-school activity?

A. Austin will go home.

B. Austin will go to swim practice.

C. Austin will go to a meeting.


D

C

F

B

E

A


D. Austin will go to track practice.

(51) 4.14 Explore the points of concurrency and their special relationships.

(51-8) Each angle of the large triangle is bisected in the figure below.

Which two small triangles are congruent?

A.

B.

C.

D.


D

C

F

B

E

A

D

CF B

E

A


(51-9) Each angle of is bisected in the figure below.

Which two triangles are congruent?

A.

B.

C.

D.

(51-10) In the diagram, each angle of is bisected.

Which two triangles are congruent?

A.

B.

C.

D.


H

EI

F

J

G

K

ED

CBA

Diagram not drawn to scale.

70°

50°

60° 65° 55°

80° 40°60°

60°


(51-11) In are midpoints.

If GI = 36, what is KG?

A. 6

B. 12

C. 18

D. 24


(52-8) Use the dimensions given in the diagram below.

What is the shortest side in the diagram?

A.

B.

C.

D.September 13,2013 Page 71

ED

CB

A

70°

50°

60° 65°60°

80° 40°55°

60°

ED

CB

A

65°

50°

65° 65°55°

70° 50°60°

60°


(52-9) Use the dimensions given in the diagram below.

What is the longest segment in the diagram?

A.

B.

C.

D.

(52-10) Use the dimensions given in the diagram.

What is the longest segment in the diagram?

A.

B.

C.


TS

RQP

70°

55°

55° 65° 55°

80°40°

60°

60°


D.

(52-11) Based on the dimensions given in the diagram, what is the longest line segment in the diagram?

A.

B.

C.

D.

(53) 1.9 Find the midpoint of a segment.

(53-8) A circle has diameter with A and B . What is the center of the circle?

A.

B.

C.

D.



(53-9) A circle has diameter with E and K . What is the center of the circle?

A.

B.

C.

D.

(53-10) has an endpoint at A and the midpoint is at M . What are the coordinates of endpoint B?

A.

B.

C.

D.

(53-11) has an endpoint at U , and the midpoint is at M . What are the coordinates of endpoint V?

A.

B.

C.

D.


(54-8) has vertices , and . What is the length of ?September 13,2013 Page 74


A.

B.

C.

D.

(54-9) has vertices , and . What is the length of ?

A.

B.

C.

D.

(54-10) Rectangle EFGH has vertices

, , and . What is the length of a diagonal?

A.

B.

C.

D.

(54-11) Rectangle MHRG has vertices

, , , and . What is the length of diagonal ?

A.

B.

C.

D.

(55) 4.15 Write an indirect proof.


W

ACP

N

RC T



Given: is not an altitude from and .Prove: is scalene.

Which contradiction must you prove for an indirect proof?

A. is an altitude

B. is a perpendicular bisector

C. is scalene

D. is isosceles



A DC

B


Given: is not a bisector of .

.Prove: is scalene.What is the assumption to be used in an indirect proof?

A. is scalene.

B. is right.

C. is acute.

D. is isosceles.


Given: is not an altitude from and .Prove: is scalene.STATEMENTS REASONS

1. is not scalene 1.

2. is isosceles 2.

3. 3.

4. is an altitude 4.

5. is not an altitude 5.

6. is scalene 6.

What is the reason for step #6?A. AssumptionB. ContradictionC. Definition of a scalene triangleD. Definition of an altitude

(55-11) In an indirect proof, after assuming the opposite of the “Proof Statement” (conclusion), the next step in the process is to



A. find a contradiction

B. prove the false assumption

C. prove the given information

D. use CPCTC

(56) 4.15 Write an indirect proof.

(56-8) What do you use as a given in an indirect proof?

A. Prove

B. Contradiction

C. CPCTC

D. Assumption

(56-9) What is the reason on the last step of an indirect proof?

A. Prove

B. Contradiction

C. CPCTC

D. Assumption

(56-10) What assumption must you make to begin an indirect proof?

A. Corresponding parts are congruent.

B. The conditions are a contradiction.

C. The given condition is false.

D. The negation of the statement to be proved.

(56-11) To begin an indirect proof, an initial assumption is made. If one were trying to prove that x = 9, what should be the initial assumption?

A. x = 9

B. x < 9

C. x > 9

D.

(57) 5.9 Utilize the distance, slope, and midpoint formulas to classify a given quadrilateral.



(57-8) Given the points , , and , which coordinates of Z would result in parallelogram WXYZ?

A.

B.

C.

D.

(57-9) In the figure below, given .

5 10 15

-5

5

10

x

y

Which coordinates of D would result in a parallelogram?

A.

B.

C.

D.


5 10 15

5

5

10

x

y

A

B C



Which coordinates of D would result in a parallelogram?

A.

B.

C.

D.

(57-11) In the diagram, which coordinates would result in a kite?

5 10

5

10

x

y

A.

B.

C.



D.


(58-8) The nth term of a sequence is . The current term is 75. What is the next term?

A. 324B. 225C. 108D. 100

(58-9) The nth term of a sequence is 3n + 2. The current term is 20. What is the next term?

A. 21B. 23C. 27D. 30

(58-10) The nth term of a sequence is . The current term is 130. What is the next term?

A. 134B. 152C. 164D. 202

(58-11) The nth term of a sequence is . If the value of a term is 400, what is the next term?

A. 8B. 289C. 409D. 529


(59-8) In , the length of side is 13 units. Given Which is a value of x?

A. –7



B. –2

C. 7

D. 15

(59-9) In , the length of side is 5 units. Given Which is a possible value of x?

A. –2

B. –1

C. 0

D. 1

(59-10) The length of is 10. Given and , what is a possible value of x?

A. –15

B. –1

C. 15

D. 57

(59-11) Given points and , what is a possible value of x if the length of is 13?

A. –5

B. –1

C. 5

D. 12


(60-8) In isosceles , is the vertex angle. If and

, what is ?

A. 4°

B. 41°

C. 82°

D. 98°



(60-9) In isosceles triangle PQR, is the vertex angle. If and , what is ?

A. 3°

B. 21°

C. 42°

D. 138°

(60-10) In isosceles triangle RST, is the vertex angle. If and

, what is ?

A. 2.5°

B. 17.5°

C. 70°

D. 142°

(60-11) In isosceles triangle HMS, is the vertex angle. If and

, what is ?

A. 10°

B. 22°

C. 79°

D. 80°


m

n

40°

105° 12

3

4 5

p r

60°

1 2 3

45

q

6 70°

80°

50°

1

2

3

4

5

140°

1

3

2

A B

C D4


Geometry Free Response Practice

(1A) Use the diagram to find the measure of the following angles, given that :

= ________ = ________

= ________ = ________

= ________

(1B) Use the diagram to find the measure of the following angles, given that :

= ________ = ________

= ________ = ________

= ________ = ________

(1C) Use the diagram to find the measure of the following angles:

= ________ = ________

= ________ = ________

= ________

(2A) Using the figure provided, write a geometric proof.

Given: is isosceles with vertex A


1

3

2

A

B

C

D

E

4

5

6

13

2

R

S

TU

4


Prove:

(2B) Using the figure provided, write a geometric proof.

Given:

Prove:

(2C) Using the figure provided, write a geometric proof.

Given:

Prove:

(3A) Use coordinate geometry to prove that .


R

T

CA

8 6 4 2 2 4 6 8

2

2

4

6

8

x

y

B

S

R

T C

A

BS

5 5

4

2

2

4

x

y


(3B) Use coordinate geometry to prove that .

(3C) Use coordinate geometry to prove that .


R

T

C

A

B

S

10 5 5 10

10

8

6

4

2

2

4

6

8

10

x

y


Geometry Honors Free Response

(1-8) Given:

Prove: x = –3

Supply reasons for each step.

(1-9) Given:

Prove: x = 3

Supply reasons for each step.

(1-10) Given:


A B


Prove: x = –2

Justify each step.

(1-11) Given:

Prove:

Justify each step.

(2-8) Write step-by-step instructions on how to construct an angle whose measure is times the measure of the original angle.

Do the construction.

(2-9) Write step by step instructions on how to construct a segment whose length is 1.5 times the original length.

Then, do the construction on the segment below.


A B


(2-10) Answer each part.

A. Write step-by-step instructions on how to construct the midpoint of a given line segment.

B. Given segment AB, construct its midpoint.

(2-11) Answer each part.

(1) Write step-by-step instructions on how to construct an angle bisector.


A

BC


(2) Given angle ABC, construct the angle bisector.

(3-8) Show that the quadrilateral QUAD, having vertices Q(–7,–6), U(7,1), A(1,3), and D(–5,0), is an isosceles trapezoid. (A blank coordinate grid is provided.)



x

y

(3-9) Prove that the quadrilateral QUAD, having vertices Q(–1,0), U(–3,6), A(3,8), and D(5,2) is a square. (A blank coordinate grid is provided.)



x

y

(3-10) Prove quadrilateral KLMN, having vertices K(–5, –4), L(0, 8), M(7, 4), and N(8, –4) is a kite.



(A blank coordinate grid is provided.)

x

y



(3-11) Prove quadrilateral WXYZ, having vertices , , , and

is a trapezoid.

x

y


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