Practice Your Skills with Answers - Hialeah Senior High School

1 DiscoveringGeometryAn Investigative ApproachPractice your Skills with 11/1/06 11:16 AM Page iTeacher s Materials Project Editor:Elizabeth DeCarliProject Administrator:Brady GoldenCoordinating Writer:Jennifer North MorrisContributors:David Rasmussen, Ralph Bothe, Judy Hicks, Michael SerraAccuracy Checker:Dudley BrooksProduction Editor:Holly RudelitschCopyeditor:Jill PellarinEditorial Production Manager:Christine OsborneProduction Supervisor:Ann RothenbuhlerProduction Coordinator:Jennifer YoungText Designers:Jenny Somerville, Garry HarmanComposition, Technical Art, Prepress:ICC Macmillan Designer:Jill KongabelPrinter:Data ReproductionsTextbook Product Manager:James RyanExecutive Editor:Casey FitzSimonsPublisher:Steven Rasmussen 2008 by Key Curriculum Press. All rights Photo Credits: Background image: Doug Wilson/ site image: Sonda Dawes/The Image Works.

2 All other images:Ken Karp Reproduction PermissionThe publisher grants the teacher whose School has adopted Discovering Geometry,and who has received Discovering Geometry: An Investigative Approach, PracticeYour Skills with Answers as part of the Teaching Resources package for the book,the right to reproduce material for use in his or her own classroom. Unauthorizedcopying ofDiscovering Geometry: An Investigative Approach, Practice your Skillswith Answers constitutes copyright infringement and is a violation of federal law. Key Curriculum Press is a registered trademark of Key Curriculum registered trademarks and trademarks in this book are the property oftheir respective Curriculum Press1150 65th StreetEmeryville, CA in the United States of America1098765432131211100908 ISBN 978-1-55953-894-7DG4 PSA_894_ 4/28/08 7:53 PM Page iiIntroduction.

3 ViChapter 1 Lesson : Building Blocks of Geometry ..1 Lesson : Poolroom Math ..2 Lesson : What s a Widget? ..3 Lesson : Polygons ..4 Lesson : Triangles ..5 Lesson : Special Quadrilaterals ..6 Lesson : Circles ..7 Lesson : Space Geometry ..8 Lesson : A Picture Is Worth a Thousand Words ..9 Chapter 2 Lesson : Inductive Reasoning ..10 Lesson : Finding the nth Term ..11 Lesson : Mathematical Modeling ..12 Lesson : Deductive Reasoning ..13 Lesson : Angle Relationships ..14 Lesson : Special Angles on Parallel Lines ..15 Chapter 3 Lesson : Duplicating Segments and Angles ..16 Lesson : Constructing Perpendicular Bisectors ..17 Lesson : Constructing Perpendiculars to a Line ..18 Lesson : Constructing Angle Bisectors ..19 Lesson : Constructing Parallel Lines.

4 20 Lesson : Construction Problems ..21 Lesson : Constructing Points of Concurrency ..22 Lesson : The Centroid ..23 Chapter 4 Lesson : Triangle Sum Conjecture ..24 Lesson : Properties of Isosceles Triangles ..25 Lesson : Triangle Inequalities ..26 Lesson : Are There Congruence Shortcuts? ..27 Lesson : Are There Other Congruence Shortcuts? ..28 Lesson : Corresponding Parts of Congruent Triangles ..29 Lesson : Flowchart Thinking ..30 Lesson : Proving Special Triangle Conjectures .. 11/1/06 11:16 AM Page iiiivChapter 5 Lesson : Polygon Sum Conjecture ..32 Lesson : Exterior Angles of a Polygon ..33 Lesson : Kite and Trapezoid Properties ..34 Lesson : Properties of Midsegments ..35 Lesson : Properties of Parallelograms ..36 Lesson : Properties of Special Parallelograms.

5 37 Lesson : Proving Quadrilateral Properties ..38 Chapter 6 Lesson : Tangent Properties ..39 Lesson : Chord Properties ..40 Lesson : Arcs and Angles ..41 Lesson : Proving Circle Conjectures ..42 Lesson : The Circumference/Diameter Ratio ..43 Lesson : Around the World ..44 Lesson : Arc Length ..45 Exploration: Intersecting Secants, Tangents, and Chords ..46 Chapter 7 Lesson : Transformations and Symmetry ..47 Lesson : Properties of Isometries ..48 Lesson : Compositions of Transformations ..49 Lesson : Tessellations with Regular Polygons ..50 Lessons : Tessellations ..51 Chapter 8 Lesson : Areas of Rectangles and Parallelograms ..52 Lesson : Areas of Triangles, Trapezoids, and Kites ..53 Lesson : Area Problems ..54 Lesson : Areas of Regular Polygons ..55 Lesson : Areas of Circles.

6 56 Lesson : Any Way You Slice It ..57 Lesson : Surface Area ..58 Chapter 9 Lesson : The Theorem of Pythagoras ..59 Lesson : The Converse of the Pythagorean Theorem ..60 Lesson : Two Special Right Triangles ..61 Lesson : Story Problems ..62 Lesson : Distance in Coordinate Geometry ..63 Lesson : Circles and the Pythagorean Theorem .. 11/1/06 11:16 AM Page ivvChapter 10 Lesson : The Geometry of Solids ..65 Lesson : Volume of Prisms and Cylinders ..66 Lesson : Volume of Pyramids and Cones ..67 Lesson : Volume Problems ..68 Lesson : Displacement and Density ..69 Lesson : Volume of a Sphere ..70 Lesson : Surface Area of a Sphere ..71 Chapter 11 Lesson : Similar Polygons ..72 Lesson : Similar Triangles ..73 Lesson : Indirect Measurement with Similar Triangles.

7 74 Lesson : Corresponding Parts of Similar Triangles ..75 Lesson : Proportions with Area ..76 Lesson : Proportions with Volume ..77 Lesson : Proportional Segments Between Parallel Lines ..78 Chapter 12 Lesson : Trigonometric Ratios ..79 Lesson : Problem Solving with Right Triangles ..80 Lesson : The Law of Sines ..81 Lesson : The Law of Cosines ..82 Lesson : Problem Solving with Trigonometry ..83 Chapter 13 Lesson : The Premises of Geometry ..84 Lesson : Planning a Geometry Proof ..85 Lesson : Triangle Proofs ..86 Lesson : Quadrilateral Proofs ..87 Lesson : Indirect Proof ..88 Lesson : Circle Proofs ..89 Lesson : Similarity Proofs ..90 Answers .. 11/1/06 11:16 AM Page vviIntroductionThe author and editors ofDiscovering Geometry: An Investigative Approachareaware of the importance of students developing geometry Skills along withacquiring concepts through investigation.

8 The student book includes manyskill-based exercises. These Practice your Skillsworksheets provide problemssimilar to the introductory exercises in each lesson ofDiscovering Geometry. Likethose exercises, these worksheets allow students to Practice and reinforce theimportant procedures and Skills developed in the lessons. Some of these problemsprovide non contextual Skills Practice . Others give students an opportunity toapply geometry concepts in fairly simple, straightforward contexts. Some are morecomplex problems that are broken down into small might assign the Practice your Skillsworksheet for every lesson, or only forthose lessons your students find particularly difficult. Or, you may wish toassign the worksheets on an individual basis, only to those students who needextra help.

9 One worksheet has been provided for nearly every lesson. There areno worksheets for Chapter 0, and the optional tessellation lessons have beencombined into two worksheets. To save you the time and expense of copyingpages, you can give students the inexpensive Practice your Skills Student Workbook,which does not have Answers . Though the copyright allows you to copy pagesfrom Practice your Skills with Answersfor use with your students, the consumablePractice your Skills Student Workbookshould not be copied. Students, parents, andmentors can also download the student worksheets from 11/1/06 11:16 AM Page viLesson Building Blocks of GeometryNamePeriodDateFor Exercises 1 7, complete each 3 midpoint ofPQ is name for NS is the _____ ofSQ . the midpoint of name for SN is all pairs of congruent segments in KLMN.

10 Use the congruence symbol to write your ( 4, 8) is the midpoint ofDE .Dhas coordinates (6, 1). Find thecoordinates Exercises 10 and 11, use a ruler to draw each figure. Label thefigure and mark the congruent cm8 cmOPNSQD iscovering Geometry Practice your Skills CHAPTER 11 2008 Key Curriculum and CD with Mas the midpoint of both AB and CD .AB cm and CD , B,and Care not and CD .Cis the midpoint ofAB ,withAC ,not on AB ,is themidpoint ofAE ,with AD six points A, B, C, D, E,and F,nothree of which are collinear. Name the linesdefined by these points. How many linesare there? the figure below, {B, C, H, E} is a set offour coplanar points. Name two other setsof four coplanar points. How many sets offour coplanar points are there? 11/1/06 1:26 PM Page 1 Lesson Poolroom MathNamePeriodDateFor Exercises 1 5, use the figure at right to complete each the _____ of is the _____ of is a _____ of BAC 42 , then m CAE DAB Exercises 6 9, use your protractor to find the measure ofeach angle to the nearest RTOFor Exercises 10 12, use your protractor to draw and then label each angle with the given MNO 15 RIG 90 z 160 For Exercises 13 15, find the measure of the angle formed by the hands at each :30 For Exercises 16 and 17, mark each figure with all the given ADB 90 ,AD BD, DAB RPQ 90 ,QR TZ, RT QZ, Q TQPZTRADCB121524117108639 RPOTABCDEA2 CHAPTER 1 Discovering Geometry Practice your Skills 2008 Key Curriculum 11/1/06 1:26 PM Page 2 Lesson What s a Widget?