Reinforcement of Standards 7AF1.2, A4.0, A5.0, A11.0, A6.0 ... · s: Triangles have three sides. q: 5 ! 3 % 8 A s or q C #s and #q B s and q D #s or q ANSWERS 1. False; 12 ! ("4)

Multiple Choice PracticeMultiple Choice

1. What is the value of x2 ! 3yz if x " 3, y " 6, and z " 4?

2. Solve 2(x ! 7) " 5x # 4.

3. Is (!2, 5) a solution of 3x # 4y " 14?

4. Factor 9x2 ! 25y2.

5. Graph y " 3x # 2.

6. Find all of the solutions of 2x2 # 5x ! 3 " 0.

A #3 only C #3 and $12$

B #$12$ and 3 D no solutions

ANSWERS1. 81 5.2. #63. yes4. (3x ! 5y)(3x # 5y)

6. Cx

y

O

Chapter 1 Glencoe Geometry

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1-1Reinforcement of Standards 7AF1.2, A4.0, A5.0, A11.0, A6.0, A14.0

Multiple Choice

Refer to the figure for Questions 1–5.1. Name three collinear

points.

2. What is another name forAB!"#?

3. Name a line in plane Z .

4. Name the intersection of planes Z and W.

5. How many lines are in plane Z?

6. Three lines are coplanar.What is the greatest number of intersection pointsthat can exist?

A 2 B 3 C 4 D 5

ANSWERS1. A, T, B2. BA!"#, AT!"#, BT!"#, TA!"#, TB!"#

3. Sample answer: Line ! or AT!"#

4. Sample answer: AT!"#

5. infinitely many6. B

Z

W!

B

Q

A T


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1-2(over Lesson 1-1)

Standard 1.0

Multiple Choice

1. Find the precision for a measurement of 42 centimeters.

2. If M is between L and N, LN " 3x ! 1, LM " 4,and MN " x ! 1, find x and MN.

3. Use the figure to find RT.

Use the figure to determine whether each pair of segmentsis congruent.4. M!N!, Q!M! 5. M!Q!, N!Q!

6. If A!B! " B!C!, AB " 4x # 2,and BC " 3x ! 3, find x.

A 5 B 4 C 3 D 2

ANSWERS1. 41.5 cm to 42.5 cm2. x " 2, MN " 13. 8$

38$ in.

4. yes5. no6. A

N

Q

M 6 cm

8 cm

8 cm


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R T

25–8 in. 53–

4 in.

S

Standard 16.0

Multiple Choice

Use the number line to find each measure.

1. AC 2. DE

3. Use the number line to find the midpoint of E!G!.

4. Find the distance between P(!2, 5) and Q(4, !3).

5. Find the coordinates of R if M(!4, 5) is themidpoint of R!S! and S has coordinates (0, !10).

6. What is the perimeter oftriangle DEF if its vertices are D(!2, !6), E(!2, 6),and F(3, !6)?

A 12 units C 17 units

B 13 units D 30 units

ANSWERS1. 42. 93. F4. 105. (#8, 20)6. D

D E F G H

D A C E

#4 #2 0 2 4 6 8 10


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Preparation for Standard 17.0

Multiple Choice

Refer to the figure for Questions 1–5.1. Name the vertex of !3.

2. Name a point in the interior of!ACB.

3. Name the sides of !BAC.

4. Name an angle with vertex B that appears to beacute.

5. If BD""# bisects !ABC, m!ABD " 2x # 3, and m!DBC " 3x ! 13, find m!ABD.

6. If P is in the interior of!MON and m!MOP " $

12$m!MON, what can you

conclude?

A !PON " !NOM

B !MON is an acute angle.

C OP""# is the angle bisector of !MON.

D m!MOP % m!PON

ANSWERS1. C 4. !ABC, !ABD, or !DBC2. G 5. 353. AB""#, AC""# 6. C

A

G

DC

B

3


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Standard 16.0

Multiple Choice

Refer to the figure for Questions 1–3.1. Name two acute vertical angles.

2. Name a linear pair whose vertex is E.

3. Name an angle supplementary to !BEC.

4. If !1 and !2 are a pair of supplementary angles,and the measure of !1 is twice the measure of!2, find the measures of both angles.

5. If R!S! ! S!T! and SV""# is the angle bisector of !RST,what is m!TSV?

6. If two angles are bothcongruent and supplementary, they must be .

A two right angles

B two acute angles

C two obtuse angles

D an obtuse and an acute angle

ANSWERS1. !AEB and !DEC2. Sample answer: !AEB, !AED3. !CED or !BEA4. m!1 " 120, m!2 " 605. 45 6. A

?

E

A

B C

D

48&


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Multiple Choice

Refer to the figures for Questions 1–5.1. Name polygon A by its number

of sides.

2. Name polygon B by its numberof sides.

3. Find the perimeter of polygon A.

4. Find the perimeter of polygon B.

5. Classify the polygons as regularor irregular.

6. What is the area ofrectangle FGHJ if its vertices are F(!3, 2), G(4, 2),H(4, !3), and J(!3, !3)?

A 24 square units

B 35 square units

C 49 square units

D 25 square units

ANSWERS1. octagon 4. 42 in2. pentagon 5. polygon A: regular, polygon

B: irregular3. 40 cm 6. B

B

8 in.

9 in.

A

5 cm


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Standards 8.0, 10.0

Multiple Choice

1. Refer to the figure. Identify the solid.

2. Find the distance between A(!3, 7)and B(1, 4).

3. Find m!C if !C and !D aresupplementary, m!C " 3y ! 5, and m!D " 8y # 20.

4. Find SR if R is the midpoint of S!U!.

5. Find n if WX!!" bisects !VWY.

6. Find the coordinates of the midpoint of M!N! if M(3, 6) and N(9, !4).

A (12, 2) B (6, 5) C (1, 6) D (6, 1)

ANSWERS1. rectangular pyramid 4. 222. 5 5. 103. 40 6. D

R

UV S

T


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2-1(over Chapter 1)

S U

6a ! 4 2(5a " 4)

R

V

X

Y

W (4n ! 8)#

(8(n " 4))#

Standard 16.0, Preparation for Standard 13.0

Multiple Choice

Make a conjecture about the next item in eachsequence.1. 1, 4, 9, 16, 25

2. $23$, $

34$, $

45$, $

56$, $

67$

Determine whether each conjecture is true orfalse. Give a counterexample for any falseconjecture.3. Given: "ABC with m!A " 60, m!B " 60, and

m!C " 60.

Conjecture: "ABC is equilateral.

4. Given: !1 and !2 are supplementary angles.Conjecture: !1 and !2 are congruent.

5. Given: "RST is isosceles.Conjecture: R!S! " S!T!

6. Make a conjecture aboutthe next item in the sequence: 64, !32, 16, !8, 4.

A !4 B !2 C 2 D 4

ANSWERS1. 36 4. False; m!1 % 70 and m!2 % 110.

2. $78$ 5. False; R!S! " R!T!.

3. true 6. B


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Standards 1.0, 3.0

Multiple Choice

Use the following statements to write acompound statement for each conjunction ordisjunction. Then find its truth value.

p: 12 ! "4 # 8q: A right angle measures 90 degrees.r: A triangle has four sides.1. p and r 2. q or r 3. #p or r

4. q and #r 5. #p or #q

6. Given the followingstatements which compound statement is false?

s: Triangles have three sides. q: 5 ! 3 % 8

A s or q C #s and #q

B s and q D #s or q

ANSWERS1. False; 12 ! ("4) % 8, and a triangle has four sides.2. True; a right angle measures 90 degrees, or a

triangle has four sides.3. False; 12 ! ("4) & 8, or a triangle has four sides.4. True; a right angle measures 90 degrees and a

triangle does not have four sides.5. False; 12 ! ("4) & 8, or a right angle does not

measure 90 degrees.6. C


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Standard 3.0

Multiple Choice

Identify the hypothesis and conclusion of eachstatement.1. If 6x ! 5 " 19, then x " 4.

2. A polygon is a hexagon if it has six sides.

Write each statement in if-then form.3. Exercise makes you healthier.

4. Squares have 4 sides.

5. Which statementrepresents the inverse of the statement If !A is aright angle, then m!A " 90?

A If !A is a right angle, then m!A " 90.

B If m!A " 90, then !A is a right angle.

C If !A is not a right angle, then m!A & 90.

D If m!A & 90, then !A is not a right angle.

ANSWERS1. Hypothesis: 6x " 5 % 19; Conclusion: x % 42. Hypothesis: a polygon has six sides

Conclusion: the polygon is a hexagon3. If you exercise, then you will be healthier.4. If a figure is a square, then it has 4 sides.5. CChapter 2 Glencoe Geometry

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Standard 3.0

Multiple Choice

Determine whether the stated conclusion isvalid based on the given information. If not,write invalid.1. Given: !A and !B are supplementary.

Conclusion: m!A # m!B " 180

2. Given: Polygon RSTU is a quadrilateral.Conclusion: Polygon RSTU is a square.

3. Given: "ABC is isosceles.Conclusion: "ABC has at least two congruentsides.

4. Given: !A and !B are congruent.Conclusion: !A and !B are vertical.

5. Given: m!Y in "WXY " 90.Conclusion: "WXY is a right triangle.

6. Which is a valid conclusionfor the statement !R and !S are vertical angles?

A m!R ! m!S % 180 C !R and !S are adjacent.B m!R ! m!S % 90 D !R " !S

ANSWERS1. valid 4. invalid2. invalid 5. valid3. valid 6. D


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Standards 1.0, 3.0

Multiple Choice

In the figure shown, A, C, andand DH#!" lie in plane R , and Bis on AC#!". State the postulatethat can be used to showeach statement is true.1. A, B, and C are collinear. 2. AC#!" lies in plane R .

3. A, H, and D are coplanar. 4. E and F are collinear.

5. DH#!" intersects EF#!" at point B.

6. Which statement is notsupported by a postulate?

A R and S are collinear.

B M lies on LM#!".

C P, X, and Y must be collinear.

D J, K, and L are coplanar.

ANSWERS1. A line contains at least two points.2. If two points lie in a plane, then the entire line

containing those points lies in that plane.3. Through any three points not on the same line,

there is exactly one plane.4. Through any two points, there is exactly one line.5. If two lines intersect, then their intersection is

exactly one point. 6. C

RF

ED

A

CB

H


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Standards 1.0, 2.0, 3.0

Multiple Choice

State the property that justifies eachstatement.1. 2(LM # NO) " 2LM # 2NO

2. If m!R " m!S, then m!R # m!T "m!S # m!T.

3. If 2PQ " OQ, then PQ " $12$ OQ.

4. m!Z " m!Z

5. If BC " CD and CD " EF, then BC " EF.

6. Which property justifiesthe statement if 90 " m!I, then m!I " 90?

A Substitution Property

B Reflexive Property

C Symmetric Property

D Transitive Property

ANSWERS1. Distributive Property2. Addition Property3. Division Property4. Reflexive Property5. Transitive Property6. C


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Standards 2.0, 3.0

Multiple Choice

Justify each statement with a property ofequality or a property of congruence.1. If A!B! " C!D! and C!D! " E!F!, then A!B! " E!F!.

2. R!S! " R!S!3. If H is between G and I, then GH # HI " GI.

State a conclusion that can be drawn from thestatements given using the property indicated.4. W is between X and Z; Segment Addition

Postulate.

5. L!M! " N!O! and N!O! " P!Q!; Transitive Property ofCongruence.

6. Which statement is true,given that K is between J and L?

A JK # KL " JL C LJ # JK " LK

B JL # LK " JK D J!K! " K!L!

ANSWERS1. Transitive Property2. Reflexive Property3. Segment Addition Postulate4. XW ! WZ % XZ5. L!M! " P!Q!6. A


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Standard 4.0

Multiple Choice


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3-1(over Chapter 2)

1. Make a conjecture about the next number in thesequence, 5, 20, 80, 320.

2. Write the contrapositive of this statement. If youlive in Boston, then you live in Massachusetts.

3. Use the Law of Detachment or the Law of Syllogismto determine whether a valid conclusion can bereached from the following set of statements.If two angles form a linear pair and are congruent,they are both right angles.!A and !B are both right angles.

4. Name the property that justifies the statement.If m!1 ! m!2 " 75 and m!2 " m!3, then m!1 ! m!3 " 75.

5. Find m!1 and m!2 if m!1 " 8x ! 18and m!2 " 16x # 6.

6. The measures of twocomplementary angles are in the ratio 7:8. What isthe measure of the larger angle?

A 42 B 48 C 84 D 96

ANSWERS1. 12802. If you do not live in Massachusetts, then you do

not live in Boston.3. no conclusion 5. m!1 " 74, m!2 " 1064. Substitution Property 6. B

1 2

Standards 2.0, 3.0

Multiple Choice

Refer to the figure.1. Name all planes parallel to

plane MNR.

2. Name all segments skew to M!P!.

Give the special name for each angle pair in the figure.3. !1 and !5

4. !3 and !8

5. !4 and !6

6. How many pairs ofalternate interior angles are there in the figureabove?

A 1 B 2 C 3 D 4

ANSWERS1. plane POS (can be named with any three letters

from POST )2. T!S!, Q!R!, N!R!, O!S!3. corresponding angles4. consecutive interior angles5. alternate exterior angles6. B

m

n

!

1

2

56 7

8

3

4

P

M N

R

ST

Q

O


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Multiple Choice

In the figure, m!4 " 146. Find the measure of each angle.1. !2

2. !7

3. !10

4. !11

5. Find m!11 ! m!6.

6. In the figure below, whatis the measure of !ABC?

A 90 B 77 C 42 D 35

ANSWERS1. 1462. 343. 1464. 345. 1806. B

p

q

A

B

C35$

42$

m

r

s

!

12

5 634

111413

10

7 812

91615


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Standard 7.0

Multiple Choice


Find the slope of each line for M(#3, 4) andN(5, #8).1. MN!"#

2. a line perpendicular to MN!"#

3. a line parallel to MN!"#

Graph the line that satisfies each condition.4. slope " 4 and contains (1, 2)

5. slope " 0 and contains (#3, #4)

6. Use slope to find a relationship between CD!"# and EF!"# for C(4, 5), D(#1, 15), E(#4, #6), and F(0, #8).

A CD!"# || EF!"# C neither || nor !

B CD!"# ! EF!"# D not enough information given

ANSWERS 1. # %32% 2. %

23% 3. # %

32%

4. 5.

6. C

x

y

O

(#3, #4)x

y

O

(1, 2)

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Reinforcement of Standard A8.0

Multiple Choice

Write an equation in point-slope form of the linehaving the given slope that contains the givenpoint.1. m " %

34%, (5, #2)

2. m " 3, (#2, 7)

Write an equation in slope-intercept form for each line.3. line with slope #3 containing (0, 2.5)

4. line with slope # %12% containing (4, #6)

5. line through (1, 5) and (3, 11)

6. Which of the following describes the line y " #%

23%x ! 6?

A parallel to the line y " %32%x ! 6

B perpendicular to the line y " #%32%x ! 6

C x-intercept is 6; y-intercept is 9.

D x-intercept is 9; y-intercept is 6.

ANSWERS1. y ! 2 " %

34%(x # 5) 4. y " #%

12%x # 4

2. y # 7 " 3(x ! 2) 5. y " 3x ! 23. y " #3x ! 2.5 6. DChapter 3 Glencoe Geometry

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Multiple Choice


Given the following information, determine whichsegments, if any, are parallel. State the postulateor theorem that justifies your answer.1. !9 " !132. !2 " !53. m!2 ! m!4 " 1804. !5 " !14

5. Refer to the figure above. Find x so that A!B! || H!I! if m!1 " 4x ! 6 and m!14 " 7x # 27.

6. If !, m, and p are coplanarlines such that ! ! p and p ! m, which statementis valid?

A m || ! C m ! !

B p || m D ! and m intersect.

ANSWERS1. F!G! || H!I!; if corr. " are ", lines are ||.2. none3. A!B! || C!D!; if consec. int. " are supp., lines are ||.4. C!D! || H!I!; if alt. int. " are ", lines are ||.5. 116. A

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3-6(over Lesson3-5)

1

2

3

4

5

67 8

9

1011

1213

14

A

B

C

D

E

F

G

H

I

Standards 7.0, 16.0

Multiple Choice

Refer to the figure.1. What is the special name

given to the pair of angles shown by !2 and !6?

2. Find m!3.

3. Find m!4.

4. Find the slope of the line that contains the pointsat (4, 4) and (2, !5).

5. Write the equation of a line in slope-intercept formthat has a slope of !

34! and contains the point at (0, 5).

6. What is the slope of a linethat is perpendicular to the line y " !

23!x ! 5?

A "!32! B "!

23! C !

23! D !

32!

ANSWERS1. corresponding angles2. 623. 1184. !

92!

5. y # !34!x $ 5

6. A

m

!1 2

5 67 118%

3 4


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4-1(over Chapter 3)

Standard 7.0; Reinforcement of Standard A8.0

Multiple Choice

Refer to the figure.1. Classify "RST as acute,

equiangular, obtuse, or right.

2. Find y if "RST is anisosceles triangle with R!S! " R!T!.

Refer to the figure.3. Find x if "ABC is an equilateral

triangle.

4. Name the right triangles ifA!D! ! C!B!.

5. Classify "MNO as scalene, isosceles, orequilateral if MN " 12, NO " 9, and MO " 15.

6. Choose the anglemeasures that represent the angles of an obtusetriangle.

A 45, 45, 90 C 50, 70, 60

B 60, 60, 60 D 30, 50, 100

ANSWERS1. obtuse 4. "ADC and "ADB2. 12 5. scalene3. 4 6. D

6x $ 5 4x $ 13

8x " 3

C BD

A

39%

5y $ 6 3(2y " 2)

39%

102%

S T

R


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Standard 12.0

Multiple Choice

Find the measureof each angle.1. m!1

2. m!2

3. m!3

4. m!4

5. m!5

6. Two angles of a trianglemeasure 46 and 65. What is the measure of the third angle?

A 65 C 111

B 69 D 115

ANSWERS1. 1152. 723. 574. 185. 1226. B

S T

V

R U

33%

75%

40%

1

2

3 4 5


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Standard 13.0

Multiple Choice

Refer to the figure.1. Identify the congruent

triangles.

2. Name the correspondingcongruent angles for the congruent triangles.

3. Name the corresponding congruent sides for the congruent triangles.

Refer to the figure.4. Find x.

5. Find m!A.

6. Find m!P if "OPQ ""WXY and m!W " 80, m!X " 70, m!Y " 30.

A 30 B 70 C 80 D 100

ANSWERS1. "LMN " "RTS 4. 32. !L " !R, !N " !S, !M " !T 5. 633. L!M! " R!T!, L!N! " R!S!, N!M! " S!T! 6. B

S

R

TL

MN


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A

CB

D

E

F

"ABC " "DEF

(9y $ 18)%

6x $ 5 9x " 4(12y $ 3)%

Standard 5.0

Multiple Choice

Determine which postulate can be used toprove that the triangles are congruent. If it isnot possible to prove that they are congruent,write not possible.1. 2.

3. 4.

5.

6. If A!B! " R!S! and B!C! " S!T!,what additional congruence statement would benecessary to prove that "ABC " "RST by theSAS postulate?

A !A " !R C !A " !T

B !C " !T D !B " !S

ANSWERS1. SAS 4. not possible2. SSS 5. SSS3. SSS 6. D


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Standard 5.0

Multiple Choice

Refer to the figure. Completeeach congruence statementand the postulate or theoremthat applies.1. "WXY " " by .

2. "WYZ " " by .

3. "VWZ " " by .

4. What additionalcongruence statement is necessary to prove"RST " "UVW by the ASA Postulate?

A !T " !W C S!T! " U!W!B !R " !U D R!T! " V!W!

ANSWERS1. "VZY, ASA or AAS2. "VYX, AAS3. "WVX, ASA, AAS, SSS, or SAS4. A

S T W V

R U

??

??

??

Z V

W X

Y


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Standard 5.0

Multiple Choice

Refer to the figure.1. Name two congruent segments

if !1 " !2.

2. Name two congruent angles ifR!S! " R!T!.

3. Find m!R if m!RUV " 65.

4. Find m!C if "ABC is isosceles with A!B! " A!C! and m!A " 70.

5. Find x if "LMN is equilateral with LM " 2x ! 4, MN " x # 6, and LN " 3x ! 14.

6. Find the measures of thebase angles of an isosceles triangle if the measureof the vertex angle is 58.

A 32 B 58 C 61 D 122

ANSWERS1. U!W! " V!W!2. !S " !T3. 504. 555. 106. C

S

U V

T

R

W

1 2


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Standard 4.0

Multiple Choice

Refer to the figure.1. Classify the triangle as scalene,

isosceles, or equilateral.

2. Find x if m!A ! 10x " 15, m!B ! 8x # 18, and m!C ! 12x " 3.

3. Name the corresponding congruent angles if "RST ! "UVW.

4. Name the corresponding congruent sides if "LMN ! "OPQ.

5. Find y if "DEF is an equilateral triangle and m!F ! 8y " 4.

6. What is the slope of theline that contains (#2, 5) and (1, 3)?

A !"32" B !"

23" C "

23" D "

32"

ANSWERS1. isosceles2. 63. !R ! !U, !S ! !V, !T ! !W4. L"M" ! O"P", M"N" ! P"Q", L"N" ! O"Q"5. 76. B

C

15 15

8A

B


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5-1(over Chapter 4

Standards 5.0, 12.0; Reinforcement of Standard A8.0

Multiple Choice

In the figure, A is the circumcenter of "LMN.1. Find y if LO ! 8y " 9 and

ON ! 12y # 11.

2. Find x if m!APM ! 7x " 13.

3. Find r if AN ! 4r # 8 and AM ! 3(2r # 11).

In "RST, R"U" is an altitude and S"V" is a median.4. Find y if m!RUS ! 7y " 27.

5. Find RV if RV ! 6a " 3 and RT ! 10a " 14.

6. Which congruencestatement is true if P is the circumcenter of"WXY?

A W"X" ! X"Y" C W"P" ! W"X"B W"P" ! X"P" D W"Y" ! X"Y"

ANSWERS1. 5 4. 92. 11 5. 273. 12.5 6. B

ST

R

V

U

M

A

N

L

O Q

P


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Standard 12.0

Multiple Choice

Determine the relationship between the lengths of thegiven sides.1. R"S", S"T" 2. R"T", S"T"

Determine the relationship between the measures of thegiven angles.3. !A, !B 4. !B, !C

Refer to the figure.5. Use the Exterior Angle Inequality

Theorem to list all angles whosemeasures are less than m!1.

6. Which angle has the greatest measure?

A !1 C !3

B !2 D !4

ANSWERS1. RS # ST 4. m!B # m!C2. RT $ ST 5. !3, !4, !5, !63. m!A # m!B 6. A

4 2 1

3

67

54 2 1

3

1215

6

A

C B

T S

R

55% 63%

62%


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Standards 12.0, 13.0

Multiple Choice

Write the assumption you would make to startan indirect proof of each statement.1. "ABC ! "DEF

2. R"S" is an angle bisector.

3. !X is a right angle.

4. If 4x # 3 & 9, then x & 3.

5. "MNO is an equilateral triangle.

6. Which statement is acontradiction to the statement that !W and !Vare vertical angles?

A !W ! !V C m!W $ m!V

B m!W ! 85 D !W is acute

ANSWERS1. "ABC # "DEF2. R"S" is not an angle bisector.3. !X is not a right angle.4. x $ 35. "MNO is not an equilateral triangle.6. C


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Standard 2.0

Multiple Choice

Determine whether the given measures can bethe lengths of the sides of a triangle. Write yesor no.1. 5, 7, 8

2. 4.2, 4.2, 8.4

3. 3, 6, 10

Find the range for the measure of the third sideof a triangle given the measures of two sides.4. 4 and 13

5. 8.3 and 15.6

6. Which value cannot bethe measure of the third side of a triangle if twosides measure 8 and 17?

A 15 B 19 C 22 D 26

ANSWERS1. yes2. no3. no4. 9 # n # 175. 7.3 # n # 23.96. D


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Standard 6.0

Multiple Choice

1. State whether this sentence is always, sometimes,or never true: The three altitudes of a triangleintersect at a point inside the triangle.

2. Find n and list the sides of !PQR in order from shortest to longest if m"P ! 12n " 15, m"Q ! 7n # 26, and m"R ! 8n " 47.

3. State the assumption you would make to start anindirect proof of this statement: If "2x ! 18, thenx " "9.

4. Find the range for the measure of the third side ofa triangle given that the measures of two sides are43 and 29.

5. Write an inequality relating m"ABD and m"CBD.

6. Which statement about the value of x is not true?

A x # 71 C x $ 48

B x # 48 ! 71 D 71 " x ! 48

ANSWERS1. sometimes 5. m"ABD # m"CBD2. 8; P!Q!, Q!R!, P!R! (or m"CBD $ m"ABD)3. x $ %9 6. C4. 14 # n # 72

48&

71&x&

A

C

B D

10

11

85

5


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6-1over Chapter 5

Standards 2.0, 6.0, 12.0

Multiple Choice

Find the measure of an interior angle given thenumber of sides of each regular polygon.1. 10

2. 12

Find the sum of the measures of the interiorangles of each convex polygon.3. 20-gon

4. 16-gon

5. Find x if QRSTU is a regularpentagon.

6. What is the measure ofthe interior angle of a regular hexagon?

A 90 B 108 C 120 D 135

ANSWERS1. 144 4. 25202. 150 5. 123. 3240 6. C

(8x ' 12)&

Q

RU

ST


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Standard 12.0

Multiple Choice

Complete each statement about #ABCD. Justify your answer.1. A!B! "2. A!D! "3. "D "

In the figure, RSTU is a parallelogram. Find the indicated value.4. x 5. y

6. Which congruence statement is not necessarily true if WXYZ is a parallelogram?

A W!Y! " X!Z! C "W " "Y

B W!X! " Y!Z! D "X " "Z

ANSWERS1. D!C!; opposite sides of a parallelogram are congruent.2. B!C!; opposite sides of a parallelogram are

congruent.3. "B; opposite angles of a parallelogram are

congruent.4. 4 5. 8 6. A

R 6(x ' 5)(12y ' 19)&

(8y ' 1)&12x ' 6

S

TU

?

?

?


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A B

CD

W X

YZ

Standard 7.0

Multiple Choice

Determine whether each quadrilateral is aparallelogram. Justify your answer.1. 2.

Determine whether a figure with the givenvertices is a parallelogram. Use the methodindicated.3. A(3, 7), B(9, 10), C(10, 6), D(4, 3); Distance Formula

4. R(2, 3), S("1, 2), T("1, "2), U(2, "2); Slope Formula

5. Which set of statements will prove that LMNOis a parallelogram?

A L!M! || N!O! and L!O! " M!N!B L!O! || M!N! and L!O! " M!N!C L!M! " L!O! and O!N! " M!N!D L!O! " M!N! and L!O! " O!N!

ANSWERS1. Yes; diagonals bisect each other.2. Yes; both pairs of opposite angles are congruent.3. yes4. no; R!S! ⁄|| U!T! 5. B

ML

O N


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Standard 7.0

Multiple Choice

WXYZ is a rectangle. Find each value.1. If ZX ! 6x " 4 and WY ! 4x # 14,

find ZX.

2. If WY ! 26 and WR ! 3y # 4, find y.

3. If m"WXY ! 6a2 " 6, find a.

RSTU is a rectangle. Find each value.4. m"VRS

5. m"RVU

6. What are the coordinatesof W if WXYZ is a rectangle and X(2, 6), Y(4, 3),and Z(1, 1)?

A (1, 4) C (%1, 4)

B (%1, %4) D (1, %4)

ANSWERS1. 502. 33. (44. 525. 1046. C

U T

S

V

R

38&

Z Y

XR

W


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Standard 7.0

Multiple Choice

LMNO is a rhombus.1. Find x.

2. Find y.

QRST is a square.3. Find n if m"TQR ! 8n # 8.

4. Find w if QR ! 5w # 4 and RS ! 2(4w " 7).

5. Find QU if QS ! 16t " 14 and QU ! 6t # 11.

6. What property applies toa square, but not a rhombus?

A Opposite angles are congruent.

B Opposite sides are congruent.

C Diagonals bisect each other.

D All angles are right angles.

ANSWERS1. 7 4. 62. 12 5. 653. 10.25 6. D

T S

RU

Q

MO P

L

N

(3x ' 12)&

(5x % 2)&

(8y % 6)&


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Standard 7.0

Multiple Choice

ABCD is an isosceles trapezoid with median E!F!.1. Find m"D if m"A ! 110.

2. Find x if AD ! 3x2 " 5 and BC ! x2 # 27.

3. Find y if AC ! 9(2y " 4) and BD ! 10y # 12.

4. Find EF if AB ! 10 and CD ! 32.

5. Find AB if AB ! r # 18, CD ! 6r # 9, and EF ! 4r # 10.

6. Which statement isalways true about trapezoid LMNO with bases ofL!M! and N!O!?

A L!O! || M!N! C L!M! || N!O!B L!O! " M!N! D L!M! " N!O!

ANSWERS1. 702. (43. 64. 215. 256. C

D C

BA

E F


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Standard 7.0

Multiple Choice

Complete each statement about parallelogram LMNO.1. L!M! "2. M!N! "3. !OLM "4. M!P! "5. Find the measure of

each interior angle.

6. What is the measure ofeach interior angle of a regular pentagon?

A 90 B 108 C 120 D 135

ANSWERS1. O!N!2. L!O!3. !MNO4. O!P!5. m!A ! 65, m!B ! 115, m!C ! 65, and

m!D ! 1156. B

A B

CD

(4y " 5)# (8y $ 5)#

(4y " 5)#(8y $ 5)#

?

?

?

?O N

MLP


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7-1(over Chapter 6)

Standard 7.0

Multiple Choice

1. There are 480 sophomores and 520 juniors in ahigh school. Find the ratio of juniors to sophomores.

2. A strip of wood molding that is 33 inches long iscut into two pieces whose lengths are in the ratioof 7:4. What are the lengths of the two pieces?

Solve each proportion.

3. %6x% ! %

7824%

4. %3597% ! %1

49x%

5. %2x

4$ 1% ! %

x "8

4%

6. The ratio of the measuresof the three angles of a triangle is 13:6:17. Find themeasure of the largest angle.

A 85 B 65 C 55 D 30

ANSWERS1. 13:122. 21 in., 12 in.3. 7

4. %143% or 3.25

5. 26. A


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Reinforcement of Standard 6NS1.3

Multiple Choice

1. Determine whether the triangles are similar.Justify your answer.

2. The quadrilaterals are similar. Write a similaritystatement and find thescale factor of the largerquadrilateral to thesmaller quadrilateral.

3. The triangles are similar. Find x and y.

4. Which one of thefollowing statements is always true?

A Two rectangles are similar.

B Two right triangles are similar.

C Two acute triangles are similar.

D Two isosceles right triangles are similar.

ANSWERS1. Yes; corresponding " are " and corresponding

sides are proportional.2. quadrilateral ABCD # quadrilateral HGFE;

scale factor ! 3:2 3. x ! 8.5, y ! 9.5 4. D

5.611.9

7.5

4

x " 2

y $ 1

L

N

MQ

RP

A D E H

GFCB 1.9

2.85

5.25

3.454.052.72.3

3.5

67.4#

12

7.25

3

13

67.4#7.8

22.6#

22.6#


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Standard 11.0

Multiple Choice

Determine whether each pair of triangles issimilar. If so, write a similarity statement.Justify your answer.1. 2.

3.

4. In the figure below, if R!S! || V!T!, find y.

A "0.8 B 0.8 C 1.2 D 4.8

ANSWERS1. yes; #ABC # #EDC; AA Similarity2. no; the sides are not proportional.3. yes; #GHI # #KLJ; SSS Similarity4. B

3

58

R

U

S

TV y " 12

G I

H J K

L

4.8

9.0

7.65.7 3.6

6.75

S

R V W

U

T

4.5

12

9

3.5

A

C

B

D E


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Standards 4.0, 5.0

Multiple Choice

Refer to the figure.1. If QT ! 5, TR ! 4, and

US ! 6, find QU.

2. If TQ ! x # 1, TR ! x " 1, QU ! 10, and QS ! 15, solve for x.

Refer to the figure.3. If AB ! 5, ED ! 8, BC ! 11,

and DC ! x " 2, find x so that B!D! || A!E!.

4. If AB ! 4, BC ! 7, ED ! 5, and EC ! 13.75, determine whether B!D! || A!E!.

5. Find the value of x # y in the figure.

A 3 C 9

B 6 D 12

ANSWERS1. 7.52. 33. 19.64. yes5. B

2y " 3 2x " 1

3x $ 25y $ 6

A B C

ED

R

Q U S

T


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Standard 12.0

Multiple Choice

1. Solve the proportion !163! " !8

x!.

2. The triangles at the right are similar. Find x and y.

3. Determine whether the triangles are similar. If so, write a similaritystatement. Justify youranswer.

4. Find the perimeter of !DEF if !ABC ! !DEF, AB ! 6.3, DE ! 15.75, and the perimeter of !ABC is 26.5.

5.Refer to the figure. If MN ! 5, NO ! 3, and NP ! 7, find MQ.

A 9 C 15

B 11!23! D 18!

23!

ANSWERS1. !

532! or 17!

13! 4. 66.25

2. x " 7.8, y " 8.4 5. D3. yes; !ABC ! !EFD; SAS Similarity

O

P

NM

Q

A

B

CD E

F

4.48

2.72

2.8

1.7

4.2

2.85.6 11.7

y

x


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8-1(over Chapter 7)

Standards 5.0, 11.0; Reinforcement of Standard 6NS1.3

Multiple Choice

Find the geometric mean between each pair ofnumbers. State exact answers and answers tothe nearest tenth.1. 9 and 13

2. 2"5# and 5"5#3. Find the altitude a. 4. Find x, y, and z.

5. Which of the following is the bestestimate of the value of x?

A 2 C 11

B 10 D 12

ANSWERS1. "117# $ 10.82. "50# $ 7.13. "24# $ 4.94. x " 8; y " "80# $ 8.9; z " "320# $ 17.95. C

12 5

13x

4

xy z

20

88

3

a


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Standard 4.0

Multiple Choice

Find x.1. 2.

3. Determine whether !QRS with vertices Q(2, "3), R(0, "1), and S(4, "1) is a right triangle. If so,identify the right angle.

Determine whether each set of measures arethe sides of a right triangle. Then statewhether they form a Pythagorean triple.

4. 16, 30, 33 5. !58!, !

32!, !

183!

6. Which of the following are not the lengths of the three sides of a righttriangle?

A 25, 20, 15 C 0.7, 2.4, 2.5

B 4, 7!12!, 8 !

12! D 36, 48, 62

ANSWERS1. "95# $ 9.7 4. no; no2. "1613# $ 40.2 5. yes; no3. yes; "Q 6. D

13

38

x

127

x


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Standards 12.0, 14.0, 15.0

Multiple Choice

Find x and y.1. 2.

3. The length of the diagonal of a square is 15"2#centimeters. Find the perimeter of the square.

4. The side of an equilateral triangle measures 21inches. Find the length of an altitude of the triangle.

5. !MNP is a 45°-45°-90° triangle with right angle P.Find the coordinates of M in Quadrant II for P(2, 3)and N(2, 8).

6.In the right triangle, find CDif DE ! 5.

A 5 C

B 5"3# D 10

ANSWERS1. x " 16, y " 16"3# 4. 10.5"3# in. $ 18.19 in.2. x " 5"2#, y " 45 5. (#3, 3)3. 60 cm 6. B

5"3#!3

C D

E

3x$

6x$

10y$

x32

30$

x

y


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Standard 20.0

Multiple Choice

1. Use a graphing calculator to find tan 54°. Roundto the nearest ten-thousandth.

2. Find m"B to the nearest tenth of a degree if cos B ! 0.8926 and "B is an acute angle.

Find x. Round to the nearest tenth.3. 4.

5.

6. What isthe value of tan !?

A !152! C !1

52!

B !1123! D !1

53!

ANSWERS1. 1.3764 4. 30.82. 26.8 5. 46.23. 14.1 6. A

13!

5

139

x$

18.5

59$

x24

36$

x


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Multiple Choice

1. Name the angles of depression and elevation in the figure.

2. Find the angle of elevation of the sun when a 6-meter flagpole casts a 17-meter shadow.

3. After flying at an altitude of 575 meters, a helicopterstarts to descend when its ground distance fromthe landing pad is 13.5 kilometers. What is theangle of depression for this part of the flight?

4. The top of a signal tower is 250 feet above sealevel. The angle of depression from the top of thetower to a passing ship is 19°. How far is the footof the tower from the ship?

5. From a point 50 feet fromthe base of a tree, the angle of elevation to the topof the tree is 32°. From a point closer to the baseof the tree, the angle of elevation is 64°. Which ofthe following is the best estimate of the distancebetween the two points at which the angle ofelevation is measured?

A 15 ft B 28 ft C 29 ft D 35 ft

ANSWERS1. "URT; "STR 3. about 2.4° 5. D2. about 19.4° 4. about 726 ft


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RU

S T

Standard 19.0

Multiple Choice

Find each measure using the given measuresof !RST. Round angle measures to thenearest degree and side measures to thenearest tenth.1. Find s if m"R ! 63, m"S ! 38, and r ! 52.

2. Find m"R if m"S ! 122, s ! 10.8, and r ! 5.2.

Solve !MNP described below. Round anglemeasures to the nearest degree and sidemeasures to the nearest tenth.3. m"M ! 50, m"N ! 32, and m ! 15

4. n ! 8.5, p ! 10.8, and m"P ! 110

5. Find the perimeter of quadrilateralABCD to the nearest tenth.

A 27.6 cm C 32.0 cmB 29.8 cm D 34.6 cm

ANSWERS1. 35.92. 243. m"P " 98, n " 10.4, p " 19.44. m"N " 48, m"M " 22, m " 4.45. B

8 cm

A B

CD

54$

70$


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Preparation for Standard T13.0

Multiple Choice

1. Find the geometric mean between 8 and 15. Statethe exact answer.

2. Determine whether the numbers 6, 9, and 12 arethe sides of a right triangle.

Find each trigonometric ratio for !ABC ifm"C ! 90, AB ! x, AC ! y, and CB ! z.3. cos A

4. sin A

5. tan B

6. Which proportion wouldbe used to find m"X for !WXY if m"W ! 42, WY! 7, XY ! 6, and WX ! 9 using the Law of Sines?

A "sin

6X

" ! "sin

742" C "

sin7

X" ! "

sin642"

B "sin

9X

" ! "sin

742" D "

sin6

X" ! "

sin942"

ANSWERS1. 2!30" 4. "x

z"

2. no 5. "yz"

3. "yx" 6. C


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9-1(over Chapter 8)

Standards 4.0, 12.0, 19.0

Multiple Choice

Name the reflected image of each figure in line m .1. B"C"2. A"B"3. !AGB

4. B

5. ABCF

6. How many lines ofsymmetry are in an equilateral triangle?

A 1 C 3

B 2 D 4

ANSWERS1. D"C"2. E"D"3. !EGD4. D5. EDCF6. C

DE

A B

GC

mF


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Standard 22.0

Multiple Choice

Find the coordinates of each figure under thegiven translation.1. R"S" with endpoints R(1, "3) and S("3, 2) under the

translation right 2 units and down 1 unit

2. !ABC with vertices A("4, 3), B("2, 1), and C(0, 5)under the translation (x, y) ! (x # 3, y " 4)

3. trapezoid LMNO with vertices L(2, 1), M(5, 1), N(1, "5), and O(0, "2) under the translation (x, y) ! (x " 1, y # 4)

4. Find the translation that moves A"B" with endpoints A(2, 4) and B("1, "3) to A"#"B"#" with endpoints A#(5, 2) and B#(2, "5).

5. Which describes atranslation left 3 units and up 4 units?

A (x, y ) ! (x $ 3, y % 4) C (x, y ) ! (x $ 3, y $ 4)

B (x, y ) ! (x % 3, y % 4) D (x, y ) ! (x % 3, y $ 4)

ANSWERS1. R#(3, %4), S#(%1, 1)2. A#(%1, %1), B#(1, %3), C#(3, 1)3. L#(1, 5), M#(4, 5), N#(0, %1), O#(%1, 2)4. (x, y) ! (x $ 3, y % 2) 5. D


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Standard 22.0

Multiple Choice

Identify the order and magnitude of rotationalsymmetry for each regular polygon.1. triangle 2. quadrilateral

3. hexagon 4. 12-gon

5. Draw the image of ABCDunder a 180° clockwiserotation about the origin.

6. If the point at ("2, 4) isrotated 90° counterclockwise about the origin,what are the new coordinates?

A ("4, "2) C (2, "4)

B ("4, 2) D ("2, "4)

ANSWERS1. order 3, magnitude 120 5.2. order 4, magnitude 903. order 6, magnitude 604. order 12, magnitude 306. A

x

y

OD!C!

B!A!

x

y

OD

C

BA


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Standard 22.0

Multiple Choice

Determine whether each regular polygontessellates the plane. Explain.1. quadrilateral

2. octagon

3. 15-gon

Determine whether a semi-regular tessellationcan be created from each figure. Assume eachfigure has a side length of 1 unit.4. triangle and square

5. pentagon and square

6. Which regular polygon willnot tessellate the plane?

A triangle C pentagon

B quadrilateral D hexagon

ANSWERS1. yes, interior angle ! 902. no, interior angle ! 1353. no, interior angle ! 1564. yes5. no6. C


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Standard 22.0

Multiple Choice

Determine whether the dilation is anenlargement, reduction, or congruencetransformation with the given scale factor.1. r ! "

23" 2. r ! 24

3. r ! 1

Find the measure of the dilation image of A"B"with the given scale factor.4. AB ! 3, r ! "2 5. AB ! "

35", r ! "

57"

6.Determine the scale factor for the dilation shown.

A %3 C "13"

B %"13" D 3

ANSWERS1. reduction2. enlargement3. congruence transformation4. 6

5. "37"

6. D

x

y

O

R#

S#

T#

R

S

T

C


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Standard 11.0

Multiple Choice

Name the reflected image of each figure in line !.1. R!S!2. S!T!3. !RWT

4. Find the length of the image of M!N! under adilation with scale factor r ! "3 and MN ! 9.

5. Find the magnitude and direction of AB! for A(4, 2)and B("2, "1).

6. Which translation mapsL!M! with endpoints L("1, 3) and M(5, "4) to L!!!M!!!with endpoints L!(3, 1) and M!(9, "6)?

A (x, y) ! (x " 4, y " 2)

B (x, y) ! (x " 4, y # 2)

C (x, y) ! (x # 4, y " 2)

D (x, y) ! (x # 4, y # 2)

ANSWERS1. V!U! 4. 272. U!T! 5. 6.7, 206.6°3. !VWT 6. C

UV

R S

T!

W


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10-1(over Chapter 9)


Multiple Choice

Refer to " F.1. Name a radius.

2. Name a chord.

3. Name a diameter.

Refer to the figure. Find each measure.4. BC

5. DE

6. Which segment in " C is a diameter?

A A!C! C C!B!B C!D! D A!B!

ANSWERS1. F!L!, F!M!, F!N!, or F!O! 4. 32. L!O!, M!N!, L!N!, or O!M! 5. 133. L!N! or O!M! 6. D

A B

D

C

A F8 5 18B EC D

L

O N

MF


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Standard 8.0

Multiple Choice

In " O, B!D! is a diameter and m!AOD " 55. Findeach measure.1. m!COB

2. m!DOC

3. m!AOB

Refer to " P. Find eachmeasure. 4. mLM"

5. mMOL"

6. If the measure of an arc is68, what is the measure of its central angle?

A 34 B 68 C 112 D 136

ANSWERS1. 114 4. 1502. 66 5. 2103. 125 6. B

O

L150#

N

M

P

A

D (4x $ 18)# (10x % 6)#55# B

C

O


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Standard 7.0

Multiple Choice

The radius of " R is 35, mLM"

" 80, LM " 45, andL!M! " N!O!. Find each measure.1. mNO"

2. mNQ"

3. N!O!4. N!T!5. R!T!

6. Which congruencestatement is true if R!S! and T!U! are congruentchords of " V?

A R!S! " S!U! C S!T! " R!U!B R!S! " T!U! D R!S! " S!T!

ANSWERS1. 802. 403. 454. 22.55. 26.86. B

O

L

NQ

R

T

MP


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Standards 7.0, 21.0

Multiple Choice

Refer to the figure. Find each measure.1. m!1

2. m!2

3. m!3

4. m!4

5. In " B, find x if m!A ! 3x # 9 and m!B ! 8x " 4.

6. If an inscribed angle has a measure of 110, what is the measure of itsintercepted arc?

A 55 B 70 C 110 D 220

ANSWERS1. 60 4. 1002. 20 5. 113. 20 6. D

A

C

D

B (8x % 4)#

(3x $ 9)#

D

A

C

B 60#

40#1

2

3

4


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Standards 7.0, 21.0

Multiple Choice

Determine whether each segment is tangentto the given circle.1. B!C! 2. Q!R!

Find x. Assume that segments that appear tobe tangent are tangent.3. 4.

5.What is the measure of P!S!?

A 10 C 14

B 12 D 18

ANSWERS1. yes 4. 20#5!2. no 5. B3. 12

WX

Y20

40

x

E

GF

9

x

15

PR

Q8

6

9A

CB 6#$3

6 12


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16 RS

P 20

Standards 7.0, 21.0

Multiple Choice

Find x. Assume that any segment that appearsto be tangent is tangent.1. 2.

3. 4.

5. What is the measure of !XYZ if YZ##$

is tangent to the circle?

A 55 C 125

B 110 D 250

ANSWERS1. 70 4. 352. 125 5. C3. 110

Y

ZX

110#

x#40#110#

x#

220#

x#

50#

60#

90#

160#

x#

55#

85#

85# 135#


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Standards 7.0, 21.0

Multiple Choice

Find x.1. 2.

3. 4.

5.Find x in the figure.

A 6 C 12

B 8 D 16

ANSWERS1. 22. 33. 64. 105. B

53

2

x

18

10

8

x

4

68

x9

63

x


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x

412

Standards 7.0, 21.0

Multiple Choice

Refer to the figure.1. Name a radius.

2. Name a chord.

3. Name a diameter.

4. Find m AB! if m!ACB ! 80.

5. Write an equation of the circle with center at ("3, 2) and a diameter of 6.

6. Which word best describes R!S!?

A chord C diameter

B arc D radius

ANSWERS1. O!C! or O!D!2. A!C!, A!D!, B!C!, C!D!3. C!D!4. 1605. (x ! 3)2 ! (y " 2)2 # 96. A

R

S

A

D

C

B

O


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Standards 8.0, 17.0, 21.0

Multiple Choice

Find the perimeter and area of eachparallelogram. Round to the nearest tenth if necessary.1. 2.

3. 4.

5. Find the height and base ofthe parallelogram if the area is 168 square units.

6. Find the area of aparallelogram if the height is 8 centimeters andthe base length is 10.2 centimeters.

A 28.4 cm2 C 81.6 cm2

B 29.2 cm2 D 104.04 cm2

ANSWERS1. 48 cm, 101.1 cm2 4. 25.2 m, 39.7 m2

2. 58 ft, 204 ft2 5. 12 units, 14 units3. 58 in., 171.5 in2 6. C

x

x ! 2

6.3 m

60$

18 in.

11 in.

17 ft

12 ft45$

13 cm

11 cm


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Standard 8.0, 10.0

Multiple Choice

Find the area of each figure. Round to thenearest tenth if necessary.1. 2.

3. 4.

5. Trapezoid LMNO has an area of 55 square units.Find the height.

6. Rhombus ABCD has an area of 144 squareinches. Find AC if BD ! 16 inches.

A 8 in. C 16 in.

B 9 in. D 18 in.

ANSWERS1. 198 units2 4. 234 units2

2. 83.1 units2 5. 5 units3. 39 units2 6. D

A C

B

D

14O N

ML 8

h

13

98

1063

12

60$

9

9

11

11


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Standards 8.0, 10.0

Multiple Choice

Find the area of each regular polygon. Roundto the nearest tenth if necessary.1. a hexagon with side length of 8 centimeters

2. a square with an apothem length of 14 inches

3. a triangle with side length of 18.6 meters

Find the area of each shaded region. Assumethat all polygons are regular. Round to thenearest tenth.4. 5.

6. Find the area of a circlewith a diameter of 8 inches.

A 4% B 8% C 16% D 64%

ANSWERS1. 166.3 cm2 4. 51.4 units2

2. 784 in2 5. 92.5 units2

3. 149.8 m2 6. C

95


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Standards 8.0, 10.0

Multiple Choice

Find the area of each figure. Round to thenearest tenth if necessary.1. 2.

3. 4.

5. Find the area of the figure.

6. Find thearea of the figure.

A 112 units2 C 162.3 units2

B 136.8 units2 D 212.5 units2

ANSWERS1. 100.7 units2 4. 117.7 units2

2. 330 units2 5. 12 units2

3. 120 units2 6. C

14

8

x

y

O("2, 0)

(4, 0)

(1, 2)

(4, "2)

8

8

7

716

12

38

8

8

15 1511

1114

10


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Standard 8.0

Multiple Choice

Find the area of each polygon.1. rhombus with diagonals of 18 and 26

2. trapezoid with bases of 14 and 30 and height of 5

3. regular hexagon with sides of 18

4. square with apothem length of 9

5. regular triangle with sides of 15

6. What is the probabilitythat a point selected at random lies in the shaded area?

A 0.09 C 0.36

B 0.25 D 0.64

ANSWERS1. 234 units2

2. 110 units2

3. 841.8 units2

4. 324 units2

5. 97.4 units2

6. C


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Standards 8.0, 10.0

Multiple Choice

For each solid, draw a net and find the surfacearea.1. 2.

3. Find the surface area of a tetrahedron with edgelengths of 4 inches. Round to the nearest tenth.

4. What is the surface area of a hexahedron with edge lengths of 7 centimeters?

A 49 cm2 B 168 cm2 C 294 cm2 D 343 cm2

ANSWERS1. 248 m2 2. 160 in2

3. 27.7 in2 4. C

6

6

6

6 8 8

8

8

4 44

4

6 6

610

10

10

10

8 in.8 in.

6 in.

10 m6 m

4 m


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Reinforcement of Standard 7MG3.6

Multiple Choice

Find the lateral area of each prism.1. 2.

Find the surface area of each prism. Round tothe nearest tenth if necessary.3. 4.

5. Find the height of a rectangular prism if thesurface area is 228 square centimeters and thebase has a length of 4 centimeters and a width of 9 centimeters.

6. What is the lateral area ofa cube with edges of 5 inches?

A 100 in2 B 125 in2 C 150 in2 D 200 in2

ANSWERS1. 300 cm2 3. 494.2 mm2 5. 6 cm2. 150 in2 4. 486 m2 6. A

9 m9 m

9 m

15 mm

8 mm

10 mm

7 in.6 in.

5 in.5 in.

4 in.

4 in.

16 cm

9 cm

6 cm


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Standards 8.0, 9.0

Multiple Choice

Find the surface area of a cylinder with thegiven dimensions. Round to the nearest tenth.1. r ! 10, h ! 6

2. d ! 18, h ! 11

3. r ! 4.5, h ! 6.3

Find the surface area of each cylinder. Roundto the nearest tenth.4. 5.

6. What is the height of acylinder with radius of 4 centimeters and surfacearea of 80! square centimeters?

A 4 cm C 6 cm

B 5 cm D 8 cm

ANSWERS1. 1005.3 units2 4. 195.0 ft2

2. 1131.0 units2 5. 1407.4 cm2

3. 305.4 units2 6. C

20 cm

8 cm

6.5 ft3.2 ft


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Standards 8.0, 9.0

Multiple Choice

Find the surface area of each regular pyramid.Round to the nearest tenth if necessary.1. 2.

3. 4.

5. Find the surface area of a square pyramid withbase length of 10 feet and slant height of 8 feet.

6. What is the slant height ofa square pyramid with base lengths of 15 inchesand height of 10 inches?

A 8.75 in. B 12.5 in. C 20 in. D 25 in.

ANSWERS1. 623.2 in2 4. 825 cm2

2. 407 m2 5. 260 ft2

3. 679.8 ft2 6. B

15 cm

20 cm14 ft

10 ft

11 m

13 m

20 in.

15 in.


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Standards 8.0, 9.0

Multiple Choice

Find the surface area of each cone. Round tothe nearest tenth.1. 2.

3. 4.

5. Find the surface area of a cone with a radius of 6 feet and a slant height of 10 feet. Round to thenearest tenth.

6. Find the slant height of acone with a radius of 4 centimeters and a surfacearea of 48! square centimeters.

A 4 cm B 8 cm C 12 cm D 16 cm

ANSWERS1. 628.3 ft2 4. 221.0 m2

2. 578.7 in2 5. 301.6 ft2

3. 593.8 cm2 6. B

8 m6 m

7 in.18 in.

8 ft15 ft


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18 cm

12 cm

Standards 8.0, 9.0

Multiple Choice

Find the surface area of each figure. Round tothe nearest tenth.1. rectangular prism with length of 6 inches, width of

5 inches, and height of 4.5 inches

2. cone with slant height of 4.3 centimeters andradius of 3.5 centimeters

3. hemisphere with radius of 6 meters

Find the lateral area of each figure.4. cylinder with radius of 8 feet and height of 12 feet

5. cone with slant height of 8.5 yards and radius of3.5 yards

6. The surface area of asphere is 36! square units. What is the radius of the sphere?

A 3 units C 9 units

B 6 units D 12 units

ANSWERS1. 159 in2 4. 603.2 ft2

2. 85.8 cm2 5. 93.5 yd2

3. 339.3 m2 6. A


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Standards 8.0, 9.0

Multiple Choice

Find the volume of each prism or cylinder.Round to the nearest tenth if necessary.1. 2.

3. 4.

5. Find the volume of a rectangular prism with alength of 12 yards, a width of 14 yards, and aheight of 9 yards.

6. The volume of a cylinderis 45! cubic millimeters and the height is 5millimeters. Find the length of the diameter.

A 3 mm C 9 mm

B 6 mm D 12 mm

ANSWERS1. 120 in3 4. 203.7 ft3

2. 785.4 cm3 5. 1512 yd3

3. 1017.9 m3 6. B

7.3 ft

6.2 ft

4.5 ft15 m

12 m

10 cm

5 cm5 in.

4 in.

12 in.


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Standards 8.0, 9.0

Multiple Choice

Find the volume of each cone or pyramid.Round to the nearest tenth if necessary.1. 2.

3. 4.

5. Find the volume of a cone with a diameter of 8.4 meters and a height of 14.6 meters.

6. Find the height of a conewith a volume of 48! cubic centimeters and aradius of 6 centimeters.

A 3 cm C 6 cm

B 4 cm D 8 cm

ANSWERS1. 134.0 mm3 4. 1177.0 in3

2. 180 ft3 5. 269.7 m3

3. 428.1 ft3 6. B

12 in.

9 in.14 ft50"

5 ft9 ft

12 ft

4 mm8 mm


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Standards 8.0, 9.0

Multiple Choice

Find the volume of each sphere orhemisphere. Round to the nearest tenth.1. 2.

3. 4.

5. Find the volume of a sphere with a diameter of14.6 feet to the nearest tenth.

6. What is the radius of asphere with a volume of 288! cubic meters?

A 6 m C 36 m

B 12 m D 72 m

ANSWERS1. 268.1 in3 4. 1286.2 mm3

2. 4188.8 ft3 5. 1629.5 ft3

3. 8578.6 cm3 6. A

17 mm16 cm

20 ft4 in.


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Standards 8.0, 9.0

Multiple Choice

Refer to the two similar pyramids.1. Find the scale factor of

the two pyramids.

2. Find the ratio of thesurface areas.

3. Find the ratio of the volumes.

Determine whether each pair of solids aresimilar, congruent, or neither.4. 5.

6. If the scale factor of twosimilar solids is 2:5, find the ratio of the volumes.

A 2:5 C 4:25

B 4:10 D 8:125

ANSWERS1. 2:3 4. congruent2. 4:9 5. similar3. 8:27 6. D

9

9

66

6

45

66

5

966

4


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Standard 11.0

Documents

Reinforcement of Standards 7AF1.2, A4.0, A5.0, A11.0, A6.0 ... · s: Triangles have three sides. q: 5 ! 3 % 8 A s or q C #s and #q B s and q D #s or q ANSWERS 1. False; 12 ! ("4)