geometry - walch · line a straight path that goes on forever in two different directions line...

Geometry

Robert Taggart

®

PB MATH TB Geometry 1/10/05 4:50 PM Page i

Table of ContentsTo the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

UUnniitt 11:: LLiinneess aanndd AAnngglleessLesson 1: Points, Lines, and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . 3Lesson 2: Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Lesson 3: Equal Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Lesson 4: Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29Lesson 5: Right Triangles and the Pythagorean Theorem . . . . . . . . . 38

UUnniitt 22:: PPeerriimmeetteerr,, CCiirrccuummffeerreennccee,, aanndd AArreeaaLesson 6: Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Lesson 7: Area of Parallelograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Lesson 8: Area of Triangles and Irregular Shapes . . . . . . . . . . . . . . . . 66Lesson 9: The Parts of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Lesson 10: Finding Circumference Measurements . . . . . . . . . . . . . . . 88Lesson 11: Area of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Lesson 12: Diameter, Radius, Circumference, and Area . . . . . . . . . . 105Lesson 13: Word Problems with Perimeter,

Circumference, and Area . . . . . . . . . . . . . . . . . . . . . . . . . . 118

UUnniitt 33:: VVoolluummeeLesson 14: Volume of Rectangular Solids . . . . . . . . . . . . . . . . . . . . . . 135Lesson 15: Volume of a Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Lesson 16: Volume of a Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Lesson 17: Volume of a Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Lesson 18: Word Problems with Volume . . . . . . . . . . . . . . . . . . . . . . 153

UUnniitt 44:: CCoooorrddiinnaattee GGeeoommeettrryyLesson 19: Number Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Lesson 20: The Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Lesson 21: Graphing Lines on the Coordinate Plane . . . . . . . . . . . . 186Lesson 22: Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Lesson 23: Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Appendixes A. Review of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220B. Review of Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221C. Review of Rules and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222D. Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Geometry

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PB MATH TB Geometry 1/10/05 4:50 PM Page iii

UNIT 1Lines and Angles

PB MATH TB Geometry 1/10/05 4:50 PM Page 1

LESSON 1: Points, Lines, and Dimensions

GOAL: To learn basic terms of geometry

WORDS TO KNOW

BBaassiicc TTeerrmmss

GGeeoommeettrryy is a kind of math that deals with points, lines, angles,planes, and shapes. The word “geometry” literally means “the measurement of the world.” Geometry is used to measurelines and shapes, and to show how they relate to one another.Geometry is used to build houses, bridges, and other structures,as well as in computer graphics, astronomy, and robotics.Everyday uses of geometry include figuring out how much carpet is needed to cover a floor, or how much water a fish tank will hold.

In this unit, you will learn about points, lines, angles, andplanes.

Everything in geometry is a series of points. A ppooiinntt is ageometric element. A point has no length, width, or height. It can only be described by its position. A point is usually namedby a capital letter, such as point A on the next page.

Lesson 1: Points, Lines, and Dimensions • Geometry

3

ddiimmeennssiioonn

eeddggeess

ggeeoommeettrryy

lliinnee

lliinnee sseeggmmeenntt

ppaarraalllleell

ppaarraalllleell lliinneess

ppllaannee

ppooiinntt

rraayy

ssoolliidd ffiigguurree


A ddiimmeennssiioonn is a measure of length, width, or height. Pointshave no actual dimensions. In books, they are usually shown as a dot. The basic forms of geometry, such as lines and planes, areall built up of points.

A lliinnee is a set of points that are joined together. They have onedimension—length. They do not have width or height. Straightlines continue forever. In geometry books, a line is usually shownas a straight line with arrows on either end, like this:

Lines are infinite. They continue forever in both directions.Usually, people do not work with the whole line. They workinstead with a part of a line. A part of a line with a beginningand an end is called a lliinnee sseeggmmeenntt.. Like a line, a line segmenthas only length. It does not have width or height. Line segmentsare usually shown with a dot at either end of the line segment,like this:

To show a line that continues forever on one end, but has anending place on the other, you would use a rraayy.. Rays, like lines

Unit 1: Lines and Angles • Geometry

4

(y-axis)

(x-axis)

Point A

3

2

1

1 2 3


and line segments, have only one dimension: length. A ray isusually shown as a line with a dot at one end and an arrow at theother end, like this:

What if you joined three line segments to form a triangleshape? You would have a second dimension—width. As soon asyou have width, you have a geometric element called a ppllaannee.. Aplane is a flat surface that has two dimensions, length and width.Unlike lines, plane figures are not infinite. They exist only in thearea you can measure. This is what a plane figure looks like in ageometry book:

Plane figures can be in any flat shape you can think of—circles, squares, rectangles, triangles, and more. Any flat shape,whether it has curved lines or straight lines, is a plane figure.

A ssoolliidd ffiigguurree adds the third dimension of depth. Solid figureshave length, width, and depth. Like a plane figure, a solid figureexists only in the area you can measure. You can measure itslength, width, and depth. Because you are reading flat paper, youcannot really see a solid figure on a page. However, we can drawa figure to make it look more solid. Here is a drawing of ageometrical solid:


5


■ PRACTICE 1: What Is Geometry?Circle the correct word or phrase to complete each sentencebelow.

11.. A point can only be defined by its aa.. position. bb.. size. cc.. shape.

22.. A line continues aa.. until it is stopped by a solid.bb.. forever in both directions.cc.. in all three dimensions.

33.. A plane figure does not haveaa.. depth. bb.. length. cc.. width.

44.. A solid figure has ___________ dimensions.aa.. 2 bb.. 3 cc.. 5

PPaarraalllleell LLiinneess

Lines are one-dimensional. They have only one measurement—the measurement of length. In this unit, you will learn about aspecial property that some lines have. Look at the diagram below.

Look at the pair of lines above. The top line (line S) is 1 inches from the bottom line (line T ). If you made lines S andT in this diagram longer, the lines would still be 1 inches apart.1

2

12

Unit 1: Lines and Angles • Geometry

6

S

T

1 inches12 1 inches1

2 1 inches12


The two lines would never cross, no matter how long you madethem. Lines that never cross and stay the same distance apart arecalled ppaarraalllleell lliinneess.. Lines S and T on the preceding page areparallel lines.

■ PRACTICE 2: Parallel LinesLook at each pair of lines below. Decide if the lines are parallel. If the lines are parallel, write parallel on the line below thediagram. If the lines are not parallel, write not parallel on theline below the diagram.

11.. __________________ 22.. __________________

33.. __________________ 44.. __________________


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Look at the following line: Is this line ppaarraalllleell? Why or why not? Can you tellfrom the information given? Write your answer ona separate sheet of paper.

THINK ABOUT IT


Geometry

WALCH PUBLISHING

Teacher’s Guide

®

Table of ContentsTo the Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viClassroom Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

UUnniitt 11:: LLiinneess aanndd AAnngglleessUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

UUnniitt 22:: PPeerriimmeetteerr,, CCiirrccuummffeerreennccee,, aanndd AArreeaaUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

UUnniitt 33:: VVoolluummeeUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

UUnniitt 44:: CCoooorrddiinnaattee GGeeoommeettrryyUnit Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Additional Activity Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Graphic Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Student Book Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Student Book Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

© 2005 Walch Publishing Algebra

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© 2005 Walch Publishing Teacher’s Guide • Geometry

1

This unit introduces the study of geometry. In Lesson 1, students learn the basic terms of geometry,such as dimensions, points, and lines. In Lesson 2, they begin to learn about angles, including rightangles, complementary angles, and supplementary angles. Lesson 3 continues the exploration ofangles, introducing students to naming angles, equal angles, and finding the measurements of angles.Lesson 4 moves on to the study of triangles, with a definition of a triangle and an explanation of theways to describe triangles. Lesson 5 introduces students to the Pythagorean theorem.

Lesson 1—Points, Lines, and DimensionsGoal: To learn basic terms of geometry

WORDS TO KNOW

ddiimmeennssiioonn a measure in one direction, such as length, width, or height

eeddggeess the line segments where two faces of a solid figure meet

ggeeoommeettrryy the area of mathematics that deals with the measurement and relationship ofpoints, lines, angles, solids, and surfaces

lliinnee a straight path that goes on forever in two different directions

lliinnee sseeggmmeenntt a part of a line that includes two points, called endpoints, and all the pointsbetween the endpoints

ppaarraalllleell lying in the same plane but not touching at any point

ppaarraalllleell lliinneess lines that are always the same distance apart but never meet

ppllaannee a flat surface or area

ppooiinntt an exact location in space, usually represented by a dot

rraayy part of a line; it has one endpoint and continues without end in one direction

ssoolliidd ffiigguurree a three-dimensional shape

Lesson 2—AnglesGoal: To learn properties of different types of angles

WORDS TO KNOW

aanngglleess figures formed by two lines that extend from the same point

Unit 1: Lines and Angles

Teacher’s Guide • Geometry © 2005 Walch Publishing

2

ccoommpplleemmeenntt the complement of an angle is the angle that, when added to the firstangle, totals 90°

ccoommpplleemmeennttaarryy aanngglleess two angles whose measures add up to 90°

ddeeggrreeeess units for measuring angles, shown with the symbol º; based ondividing a circle into 360 equal parts

ppeerrppeennddiiccuullaarr meeting at a right angle

rriigghhtt aanngglleess angles whose measure is 90°

ssttrraaiigghhtt aannggllee an angle that measures 180˚

ssuupppplleemmeenntt the supplement of an angle is the angle that, when added to the firstangle, totals 180°

ssuupppplleemmeennttaarryy aanngglleess two angles whose measures add up to 180°

Lesson 3—Equal AnglesGoal: To find equal angles and figure out the measurements of angles based on

their relationships to other angles

WORD TO KNOW

ttrraannssvveerrssaall a line that crosses two or more lines at different points

Lesson 4—TrianglesGoal: To identify different types of triangles and find the measurements of angles

in a triangle

WORDS TO KNOW

aaccuuttee aannggllee an angle that has a measure greater than 0˚ and less than 90˚

aaccuuttee ttrriiaannggllee a triangle in which all three angles are acute, that is, greater than 0°and less than 90°

eeqquuiillaatteerraall ttrriiaannggllee a triangle where all three sides are the same length

iissoosscceelleess ttrriiaannggllee a triangle in which two sides are the same length

oobbttuussee aannggllee an angle that has a measure greater than 90˚ and less than 180˚

oobbttuussee ttrriiaannggllee a triangle that has one obtuse angle (one angle that measures greaterthan 90º and less than 180º)


3

ppllaannee ffiigguurree a figure that lies on one plane; it has only two dimensions

rriigghhtt ttrriiaannggllee a triangle that has one right angle (an angle that measures 90°)

ssccaalleennee ttrriiaannggllee a triangle in which no two sides are the same length

ttrriiaannggllee a flat shape with three sides

ttwwoo--ddiimmeennssiioonnaall measured in two dimensions, or directions, such as length and width; flat

Lesson 5—Right Triangles and the Pythagorean TheoremGoal: To use the Pythagorean theorem to find the lengths of the sides of right

triangles

WORDS TO KNOW

ffoorrmmuullaa a general rule for finding the value of something; often written with variables

hhyyppootteennuussee the side of a right triangle that is opposite the right angle

lleeggss in a right triangle, the two sides that form the right (90º) angle

PPyytthhaaggoorreeaann tthheeoorreemm a statement that says that, in any right triangle, the square of the side oppositethe right angle (the hypotenuse) is equal to the sum of the squares of the othertwo sides. If one side is 2 cm long and the other side is 3 cm long, then thesquare of the hypotenuse is 22 + 32 = 4 + 9 = 13.

ssqquuaarree a number multiplied by itself

ssqquuaarree rroooott The square root of a number is the factor that, when multiplied by itself, givesthe number.

ssqquuaarree rroooott ssyymmbbooll The symbol for “square root of ” is , as in = 3.

tthheeoorreemm an important mathematical statement that can be proved to be true

NNootteess oonn AApppplliiccaattiioonn AAccttiivviittiieess iinn SSttuuddeenntt TTeexxtt

��9��

AAccttiivviittyy SSkkiillllss AApppplliieedd PPrroodduucctt

FFiinnddiinngg LLiinneess aanndd AAnngglleess gathering information drawings

preparing visual demonstrations

TTrriiaannggllee AAnngglleess visualizing shapes reconfiguredtriangle

working with others written paragraph

Teacher’s Guide • Geometry © 2005 Walch Publishing

4

AAddddiittiioonnaall AAccttiivviittyy SSuuggggeessttiioonnss■ People who work in the building trades work with lines and angles a great deal. Have learners

contact a builder or carpenter, and ask what specific skills (such as measuring and calculating)and tools (such as levels and T-squares) are used to make sure a project is done accurately andholds together. Learners could also have a builder or carpenter demonstrate how to use thesetools, or learners could demonstrate this themselves.

TTeeaacchhiinngg TTiipp■ To reinforce identification of various types of triangles, have learners search their school, home,

workplace, and so on for examples of scalene, equilateral, and isosceles triangles. Have thembring in pictures or drawings of five examples of each. They should also note which are also righttriangles.

DDiiffffeerreennttiiaattiioonn

■ Students learning geometry can get caught up in a slew of definitions, propositions, theorems,formulas, and so on. All the numbers and symbols can make everything seem very abstract. Youcan help learners see how geometry is connected to reality by taking them on a mini-field tripthrough the building. Have them observe structural congruencies, examples of parallelism, theway components of the building are made up of the figures they are studying, and so on. Thisshould help them realize that geometry is real. It is everywhere. It is not just a bunch of formulasand theorems. Once students can recognize and name geometrical figures, they’ll feel lessintimidated to work with them.

■ Preview the vocabulary in each lesson by reading the Words to Know and their definitions toyour students. For each definition, point to an object in the classroom that fits the definition.Then ask students to identify other objects that also fit the definition. This helps them have aconcrete understanding of the new concepts.


27

GGrraapphhiicc OOrrggaanniizzeerrssGraphic organizers are a versatile teaching and learning tool. They can help students clarify their thinking,integrate new knowledge, reinforce their understanding of a topic, and review material for quizzes and tests.Using graphic organizers, learners can understand content more clearly and can take clear, concise notes.Graphic organizers can also act as a visual aid to make abstract concepts more concrete.

The graphic organizers provided here can be used in many ways. You can use transparencies of theorganizers to introduce or review a topic with the entire class. You can photocopy the organizers and allowstudents to use them as they work through the student text. Here is a brief description of the organizers inthis section and their uses.

SSttrruuccttuurreedd NNootteessThis organizer is one way of organizing notes as students read through the text. Students should write themain topic in the box at the top. In the boxes underneath they can write details about the topic, specificinformation, examples, and so forth.

CCoonncceepptt aanndd DDeeffiinniittiioonn CChhaarrttThis chart is used to keep track of new vocabulary and concepts as they are introduced in the text. Studentsshould write the word or concept in the box at the top of the chart. They should then fill in the information inthe rest of the boxes.

SStteeppss iinn aa PPrroocceessss CChhaarrttThis graphic organizer is used to show information in order. Students will find this organizer particularlyuseful when taking notes of mathematical processes, showing the steps in order. They should write theprocess in the box at the top of the chart, then break the process down into steps and write one step in onebox, adding or deleting boxes as needed.

TTaabblleeThis graphic organizer has many uses. Students should label each column, then write relevant information ineach cell of the chart.

Graphic Organizers


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Concept and Definition Chart

CCoonncceepptt

CChhaarraacctteerriissttiiccss

WWhhaatt iiss iitt lliikkee?? WWhhaatt iiss iitt nnoott lliikkee??

DDeeffiinniittiioonn EExxaammpplleess

Geometry

WALCH PUBLISHING

Workbook

Table of ContentsTo the Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii

AAccttiivviittyy 11Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

AAccttiivviittyy 22Parallel Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

AAccttiivviittyy 33Measuring Line Segments . . . . . . . . . . . . . . . . . . 3

AAccttiivviittyy 44Constructing Congruent Line Segments Using a Compass . . . . . . . . . . . . . . . . . . . . . . . . . 4

AAccttiivviittyy 55Constructing Congruent Line Segments Using a Safe-Drawing Compass . . . . . . . . . . . . . 5

AAccttiivviittyy 66Angles, Angles Everywhere! . . . . . . . . . . . . . . . . 6

AAccttiivviittyy 77Acute, Obtuse, and Straight Angles . . . . . . . . . . 7

AAccttiivviittyy 88Measuring Angles . . . . . . . . . . . . . . . . . . . . . . . . 8

AAccttiivviittyy 99Constructing Perpendicular Lines . . . . . . . . . . . 9

AAccttiivviittyy 1100Using Equations to Find Complements . . . . . . 10

AAccttiivviittyy 1111Using Equations to Find Supplements . . . . . . . 11

AAccttiivviittyy 1122Complementary and Supplementary Angles . 12

AAccttiivviittyy 1133Drawing Angles . . . . . . . . . . . . . . . . . . . . . . . . . 13

AAccttiivviittyy 1144Angle Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 14

AAccttiivviittyy 1155Vertical and Adjacent Angles . . . . . . . . . . . . . . 15

AAccttiivviittyy 1166Constructing Parallel Lines . . . . . . . . . . . . . . . . 16

AAccttiivviittyy 1177Street Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

AAccttiivviittyy 1188Drawing Transversals . . . . . . . . . . . . . . . . . . . . 18

AAccttiivviittyy 1199Regular and Irregular Polygons . . . . . . . . . . . . 19

AAccttiivviittyy 2200More Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . 20

AAccttiivviittyy 2211Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . 21

AAccttiivviittyy 2222Acute and Obtuse Triangles . . . . . . . . . . . . . . . 22

AAccttiivviittyy 2233The Sum of the Angles of a Triangle . . . . . . . . 23

AAccttiivviittyy 2244The Sum of the Angles in a Quadrilateral . . . . 24

AAccttiivviittyy 2255Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

AAccttiivviittyy 2266Squares and Square Roots . . . . . . . . . . . . . . . . 26

AAccttiivviittyy 2277Drawing the Pythagorean Theorem . . . . . . . . 27

AAccttiivviittyy 2288Pythagoras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

AAccttiivviittyy 2299Using Formulas to Find the Perimeter of Rectangles and Squares . . . . . . . . . . . . . . . . 29

AAccttiivviittyy 3300Perimeter of Regular Polygons . . . . . . . . . . . . . 30

AAccttiivviittyy 3311Area and Blueprints . . . . . . . . . . . . . . . . . . . . . 31

AAccttiivviittyy 3322Relating Area and Perimeter . . . . . . . . . . . . . . 32

AAccttiivviittyy 3333Finding the Area of a Parallelogram I . . . . . . . 33

AAccttiivviittyy 3344Finding the Area of a Parallelogram II . . . . . . . 34

UUnniitt 22:: PPeerriimmeetteerr,, CCiirrccuummffeerreennccee,, aanndd AArreeaa

UUnniitt 11:: LLiinneess aanndd TTrriiaanngglleess

© 2005 Walch Publishing Geometry

iii

Geometry © 2005 Walch Publishing

iv

Table of Contents, continuedAAccttiivviittyy 3355

Finding the Area of a Triangle . . . . . . . . . . . . . 35

AAccttiivviittyy 3366Finding the Area of a Trapezoid . . . . . . . . . . . . 36

AAccttiivviittyy 3377Finding the Area of a Complex Figure . . . . . . . 37

AAccttiivviittyy 3388Drawing Circles . . . . . . . . . . . . . . . . . . . . . . . . . 38

AAccttiivviittyy 3399Radii, Circumference, and Arcs I . . . . . . . . . . . 39

AAccttiivviittyy 4400Radii, Circumference, and Arcs II . . . . . . . . . . 40

AAccttiivviittyy 4411Central Angles . . . . . . . . . . . . . . . . . . . . . . . . . . 41

AAccttiivviittyy 4422Using Equations to Find Central Angles . . . . . 42

AAccttiivviittyy 4433Central Angles and Fractions . . . . . . . . . . . . . . 43

AAccttiivviittyy 4444More about Pi (�) . . . . . . . . . . . . . . . . . . . . . . . 44

AAccttiivviittyy 4455Perimeter of Complex Figures . . . . . . . . . . . . . 45

AAccttiivviittyy 4466Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

AAccttiivviittyy 4477Making Circle Graphs . . . . . . . . . . . . . . . . . . . . 47

AAccttiivviittyy 4488Area of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . 48

AAccttiivviittyy 4499Using Radius or Diameter to Find the Area of a Circle . . . . . . . . . . . . . . . . . . . . . . 49

AAccttiivviittyy 5500Area of Complex Figures . . . . . . . . . . . . . . . . . . 50

AAccttiivviittyy 5511Changing Formulas . . . . . . . . . . . . . . . . . . . . . . 51

AAccttiivviittyy 5522Using Formulas . . . . . . . . . . . . . . . . . . . . . . . . . 52

AAccttiivviittyy 5533Algebra, Formulas, and Circles . . . . . . . . . . . . 53

AAccttiivviittyy 5544Using the Area and Circumference Formulas . 54

AAccttiivviittyy 5555Word Problems with Perimeter, Circumference, and Area . . . . . . . . . . . . . . . . . 55

AAccttiivviittyy 5566Space Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

AAccttiivviittyy 5577Polyhedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

AAccttiivviittyy 5588Platonic Solids . . . . . . . . . . . . . . . . . . . . . . . . . 58

AAccttiivviittyy 5599Finding Volume . . . . . . . . . . . . . . . . . . . . . . . . . 59

AAccttiivviittyy 6600Finding the Volume of RectangularPrisms and Cubes . . . . . . . . . . . . . . . . . . . . . . . 60

AAccttiivviittyy 6611Finding the Volume of Prisms . . . . . . . . . . . . . 61

AAccttiivviittyy 6622Visualizing the Volume of a Cylinder . . . . . . . . 62

AAccttiivviittyy 6633Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

AAccttiivviittyy 6644Finding the Volume of Cones and Pyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

AAccttiivviittyy 6655Finding the Volume of Space Figures . . . . . . . . 65

AAccttiivviittyy 6666Surface Area of Rectangular Prisms . . . . . . . . . 66

AAccttiivviittyy 6677Surface Area of Cylinders . . . . . . . . . . . . . . . . . 67

AAccttiivviittyy 6688Word Problems with Volume . . . . . . . . . . . . . . 68

UUnniitt 33:: VVoolluummee

© 2005 Walch Publishing Geometry

v

Table of Contents, continued

AAccttiivviittyy 6699Fractions on the Number Line . . . . . . . . . . . . . 69

AAccttiivviittyy 7700Property of Density . . . . . . . . . . . . . . . . . . . . . . 70

AAccttiivviittyy 7711Graphing the Solution to an Equationor an Inequality on the Number Line . . . . . . . 71

AAccttiivviittyy 7722Drawing the Coordinate Plane . . . . . . . . . . . . . 72

AAccttiivviittyy 7733The Coordinate Plane . . . . . . . . . . . . . . . . . . . . 73

AAccttiivviittyy 7744Graphing on the Four Quadrants of the Coordinate Plane . . . . . . . . . . . . . . . . . . 74

AAccttiivviittyy 7755Graphing Game . . . . . . . . . . . . . . . . . . . . . . . . . 75

AAccttiivviittyy 7766Transformations on the Coordinate Plane . . . 76

AAccttiivviittyy 7777Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

AAccttiivviittyy 7788Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . 78

AAccttiivviittyy 7799Using Intercepts to Graph Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . 79

AAccttiivviittyy 8800Graphing Nonlinear Equations . . . . . . . . . . . . 80

AAccttiivviittyy 8811Functions and Measurement . . . . . . . . . . . . . . 81

AAccttiivviittyy 8822Graphing Inequalities . . . . . . . . . . . . . . . . . . . . 82

AAccttiivviittyy 8833Slope I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

AAccttiivviittyy 8844Slope II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

AAccttiivviittyy 8855The Slope-Intercept Form of an Equation of a Line . . . . . . . . . . . . . . . . . . . . . . . 85

AAccttiivviittyy 8866Graphing a Line Using the Slope-Intercept Form of an Equation . . . . . . . . . . . . . 86

AAccttiivviittyy 8877Slope and Parallel and Perpendicular Lines . . . . . . . . . . . . . . . . . . . . . . 87

AAccttiivviittyy 8888Systems of Equations . . . . . . . . . . . . . . . . . . . . 88

AAccttiivviittyy 8899Graphing Equations and Inequalities to Solve Word Problems . . . . . . . . . . . . . . . . . . 89

UUnniitt 44:: CCoooorrddiinnaattee GGeeoommeettrryy

© 2005 Walch Publishing Unit 1: Lines and Triangles • Geometry

1

A dimension is a measure of length, width, or height. Plane figures, such as rectangles and squares,have width and length. They are two-dimensional. Objects, such as your classroom, a car, or a table,have length, width, and height. They are three-dimensional.

Look at each picture below. Decide if the object that is pictured has two dimensions or threedimensions. Write two-dimensional or three-dimensional on the line below each picture.

11.. 22..

______________________ ______________________

33.. 44..

______________________ ______________________

55.. 66..

______________________ ______________________

List three other things that are three-dimensional. Then list three other things that are two-dimensional.

77.. __________________ __________________ __________________

__________________ __________________ __________________

UNIT 1 • ACTIVITY 1DDiimmeennssiioonnss

NAME:

Unit 3: Volume • Geometry © 2005 Walch Publishing

56

A space figure is a figure with three dimensions: length, width, and height. Space figures are alsocalled solid figures and three-dimensional figures. A polyhedron (plural polyhedra) is a space figurethat is made up of polygons. You have learned about the polyhedron that is made up of rectangles.This figure is called a rectangular prism. Polyhedra are named for the shape of their bases. There aremany space figures. Look at the chart below.

Write the name of each figure on the line.

UNIT 3 • ACTIVITY 56SSppaaccee FFiigguurreess

NAME:

PPrriissmmss

A pprriissmm is a polyhedron that has two congruent and parallel bases and rectangular faces.

PPyyrraammiiddss

A ppyyrraammiidd is a polyhedron that has a base that is a polygon and other faces that are triangles thatshare a common vertex.

Other space figures are nnoott ppoollyyhheeddrraa because they have curved sides.

TTrriiaanngguullaarr PPrriissmm HHeexxaaggoonnaall PPrriissmm RReeccttaanngguullaarr PPrriissmm

RReeccttaanngguullaarr PPyyrraammiidd TTrriiaanngguullaarr PPyyrraammiidd OOccttaaggoonnaall PPyyrraammiidd

CCyylliinnddeerr CCoonnee SSpphheerree

11..

__________________________

22..

__________________________

33..

__________________________

44..

__________________________

55..

__________________________

66..

__________________________

77..

__________________________

88..

__________________________

Geometry

WALCH PUBLISHING

Test Pack

Table of ContentsTo the Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Testing Students Who Do Not Test Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Test-Taking Strategies for Power Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

PPrreetteesstt .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 11

UUnniitt 11 TTeesstt:: LLiinneess aanndd AAnngglleess .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 88

UUnniitt 22 TTeesstt:: PPeerriimmeetteerr,, CCiirrccuummffeerreennccee,, aanndd AArreeaa .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1144

UUnniitt 33 TTeesstt:: VVoolluummee .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2222

UUnniitt 44 TTeesstt:: CCoooorrddiinnaattee GGeeoommeettrryy .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2277

PPoosstttteesstt .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 3333

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Student Record-Keeping Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Strategies for Standardized Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

© 1997, 2000, 2005 Walch Publishing Geometry Test Pack

iii

Circle the correct answer for each of the following questions. Show your work, if necessary.

11.. How many degrees are there in angle A?

aa.. 70°bb.. 110°cc.. 290°dd.. 90°

22.. How many degrees are there in angle C?

aa.. 50°bb.. 40°cc.. 30°dd.. 25°

33.. A right triangle has one leg that is 10 inches long and one leg that is 5 inches long. How long isthe triangle’s hypotenuse?

aa.. 11.18 in.bb.. 1.25 in.cc.. 10 in.dd.. 15 in.

GEOMETRY • PRETESTNAME: DATE:

© 1997, 2000, 2005 Walch Publishing Pretest • Geometry Test Pack

1

AA

111100˚̊

CC

4400˚̊

Pretest • Geometry Test Pack © 1997, 2000, 2005 Walch Publishing

2

44.. A triangle has two sides of equal length. With this information only, we can say that it isaa.. a scalene triangle.bb.. an equilateral triangle.cc.. an isosceles triangle.dd.. a right triangle.

55.. A triangle has one angle that is greater than 90°. With this information only, we can say that it is

aa.. a scalene triangle.bb.. an acute triangle.cc.. a right triangle.dd.. an obtuse triangle.

66.. A triangle has three sides of equal length. With this information only, we can say that it isaa.. an equilateral triangle.bb.. an acute triangle.cc.. both an equilateral and an acute triangle.dd.. a right triangle.

77.. Which angles below are equal to angle H?

aa.. F, E, Gbb.. G, D, Ccc.. E, D, Add.. E, C, B

88.. Jonah wants to buy carpeting for his new apartment. He wants to carpet his living room and hisbedroom. The living room is 6 meters long and 4 meters wide. The bedroom is 5 meters square.How much carpeting does Jonah have to buy to cover the floors in both rooms?

aa.. 75 m2

bb.. 49 m2

cc.. 36 m2

dd.. 15 m2

NAME: DATE:

AA BBCC DD

EE FFGG HH

NAME: DATE:

Unit 1 Test • Geometry Test Pack © 1997, 2000, 2005 Walch Publishing

8

Circle the correct answer to each of the following questions. Show your work, if necessary.

11.. Which of the following objects is two-dimensional?aa.. a pair of dicebb.. a basketballcc.. a treedd.. a circle

22.. Which pair of lines below are parallel?

aa.. cc..

bb.. dd..

UNIT 1 TEST • LINES AND ANGLES

© 1997, 2000, 2005 Walch Publishing Unit 1 Test • Geometry Test Pack

9

NAME: DATE:

33.. How many angles are there in the diagram below?

aa.. 3bb.. 1cc.. 6dd.. 4

44.. How many degrees are there in angle A?

aa.. 60°bb.. 120°cc.. 240°dd.. 90°

55.. How many degrees are there in angle C?

aa.. 55°bb.. 90°cc.. 145°dd.. 180°

AA

112200˚̊

CC

3355˚̊

GEOMETRY • POSTTEST NAME: DATE:

© 1997, 2000, 2005 Walch Publishing Posttest • Geometry Test Pack

33

Circle the correct answer to each of the following questions. Show your work, if necessary.

11.. Angle A of triangle ABC measures 55° and angle B measures 40°. How much does angle Cmeasure?

aa.. 65°bb.. 75°cc.. 85°dd.. 95°

22.. What is a triangle with no equal sides called?aa.. an equilateral trianglebb.. an obtuse trianglecc.. a scalene triangledd.. an isosceles triangle

33.. What is the complement of an angle that measures 45°?aa.. 30°bb.. 45°cc.. 150°dd.. 330°

44.. Which angles below are equal to angle L?

aa.. M, P, Qbb.. O, Q , Rcc.. N, P, Rdd.. O, P, S

LL MMNN OO

PP QQRR SS

Posttest • Geometry Test Pack © 1997, 2000, 2005 Walch Publishing

34

55.. What is the area of the circle below? (� = 3.14)

aa.. 12.56 cm2

bb.. 12.56 cmcc.. 6.28 cmdd.. 6.28 cm2

66.. What is the circumference of a circle with a radius of 5 inches? (� = 3.14)aa.. 15.7 metersbb.. 23.6 meterscc.. 31.4 metersdd.. 35.4 meters

77.. What is the radius of a circle with a circumference of 62.8 meters? (� = 3.14)aa.. 2.5 metersbb.. 5 meterscc.. 10 metersdd.. 25 meters

88.. The base of the semicircle below is 12 feet. What is its area? (� = 3.14)

aa.. 30.84 square feetbb.. 37.68 square feetcc.. 56.52 square feetdd.. 78.84 square feet

NAME: DATE:

12 ft

2 cm

geometry - walch · line a straight path that goes on forever in two different directions line...

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