Transcription

CK-12 Geometry - SecondEdition, Answer KeyCK-12 FoundationSay Thanks to the AuthorsClick http://www.ck12.org/saythanks(No sign in required)

www.ck12.orgTo access a customizable version of this book, as well as otherinteractive content, visit www.ck12.orgAUTHORCK-12 FoundationCK-12 Foundation is a non-profit organization with a missionto reduce the cost of textbook materials for the K-12 marketboth in the U.S. and worldwide. Using an open-content, webbased collaborative model termed the FlexBook textbook, CK-12intends to pioneer the generation and distribution of high-qualityeducational content that will serve both as core text as well asprovide an adaptive environment for learning, powered throughthe FlexBook Platform .Copyright 2015 CK-12 Foundation, www.ck12.orgThe names “CK-12” and “CK12” and associated logos and theterms “FlexBook ” and “FlexBook Platform ” (collectively“CK-12 Marks”) are trademarks and service marks of CK-12Foundation and are protected by federal, state, and internationallaws.Any form of reproduction of this book in any format or medium,in whole or in sections must include the referral attribution linkhttp://www.ck12.org/saythanks (placed in a visible location) inaddition to the following terms.Except as otherwise noted, all CK-12 Content (including CK-12Curriculum Material) is made available to Users in accordancewith the Creative Commons Attribution-Non-Commercial 3.0Unported (CC BY-NC 3.0) License (http://creativecommons.org/licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporatedherein by this reference.Complete terms can be found at http://www.ck12.org/about/terms-of-use.Printed: February 25, 2015iii

Contentswww.ck12.orgContents12345ivBasics of Geometry, Answer Key1.1Geometry - Second Edition, Points, Lines, and Planes, Review Answers1.2Geometry - Second Edition, Segments and Distance, Review Answers .1.3Geometry - Second Edition, Angles and Measurement, Review Answers1.4Geometry - Second Edition, Midpoints and Bisectors, Review Answers .1.5Geometry - Second Edition, Angle Pairs, Review Answers . . . . . . .1.6Geometry - Second Edition, Classifying Polygons, Review Answers . .1.7Geometry - Second Edition, Chapter Review Answers . . . . . . . . . .125710131417Reasoning and Proof, Answer Key2.1Geometry - Second Edition, Inductive Reasoning, Review Answers . . . . . . . . . . .2.2Geometry - Second Edition, Conditional Statements, Review Answers . . . . . . . . .2.3Geometry - Second Edition, Deductive Reasoning, Review Answers . . . . . . . . . .2.4Geometry - Second Edition, Algebraic and Congruence Properties, Review Answers . .2.5Geometry - Second Edition, Proofs about Angle Pairs and Segments, Review Answers .2.6Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18192123262933.Parallel and Perpendicular Lines, Answer Key3.1Geometry - Second Edition, Lines and Angles, Review Answers . . . . . . . . . . . .3.2Geometry - Second Edition, Properties of Parallel Lines, Review Answers . . . . . . .3.3Geometry - Second Edition, Proving Lines Parallel, Review Answers . . . . . . . . . .3.4Geometry - Second Edition, Properties of Perpendicular Lines, Review Answers . . . .3.5Geometry - Second Edition, Parallel and Perpendicular Lines in the Coordinate Plane,Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6Geometry - Second Edition, The Distance Formula, Review Answers . . . . . . . . . .3.7Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Review. . . . . . . . . . . . .3435374042434749Triangles and Congruence, Answer key4.1Geometry - Second Edition, Triangle Sums, Review Answers . . . . . . . . . . . . . . . . . .4.2Geometry - Second Edition, Congruent Figures, Review Answers . . . . . . . . . . . . . . . .4.3Geometry - Second Edition, Triangle Congruence using SSS and SAS, Review Answers . . . .4.4Geometry - Second Edition, Triangle Congruence using ASA, AAS, and HL, Review Answers4.5Geometry - Second Edition, Isosceles and Equilateral Triangles, Review Answers . . . . . . .4.6Chapter 4 Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50515355586063Relationships with Triangles, Answer Key5.1Geometry - Second Edition, Midsegments of a Triangle, Review Answers . . . . .5.2Geometry - Second Edition, Perpendicular Bisectors in Triangles, Review Answers5.3Geometry - Second Edition, Angle Bisectors in Triangles, Review Answers . . . .5.4Geometry - Second Edition, Medians and Altitudes in Triangles, Review Answers .5.5Geometry - Second Edition, Inequalities in Triangles, Review Answers . . . . . . .5.6Geometry - Second Edition, Extension: Indirect Proof, Review Answers . . . . . .64656771737576.

www.ck12.org5.76789ContentsChapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Polygons and Quadrilaterals, Answer Key6.1Geometry - Second Edition, Angles in Polygons, Review Answers . . . . . . . . . . . .6.2Geometry - Second Edition, Properties of Parallelograms, Review Answers . . . . . . .6.3Geometry - Second Edition, Proving Quadrilaterals are Parallelograms, Review Answers6.4Geometry - Second Edition, Rectangles, Rhombuses and Squares, Review Answers . . .6.5Geometry - Second Edition, Trapezoids and Kites, Review Answers . . . . . . . . . . .6.6Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Similarity, Answer Key7.1Geometry - Second Edition, Ratios and Proportions, Review Answers . . .7.2Geometry - Second Edition, Similar Polygons, Review Answers . . . . . .7.3Geometry - Second Edition, Similarity by AA, Review Answers . . . . . .7.4Geometry - Second Edition, Similarity by SSS and SAS, Review Answers .7.5Geometry - Second Edition, Proportionality Relationships, Review Answers7.6Geometry - Second Edition, Similarity Transformations, Review Answers .7.7Geometry - Second Edition, Extension: Self-Similarity, Review Answers . .7.8Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . .77.78798183868991.92939495969799101103Right Triangle Trigonometry, Answer Key8.1Geometry - Second Edition, The Pythagorean Theorem, Review Answers . . . . . .8.2Geometry - Second Edition, Converse of the Pythagorean Theorem, Review Answers8.3Geometry - Second Edition, Using Similar Right Triangles, Review Answers . . . . .8.4Geometry - Second Edition, Special Right Triangles, Review Answers . . . . . . . .8.5Geometry - Second Edition, Tangent, Sine and Cosine, Review Answers . . . . . . .8.6Geometry - Second Edition, Inverse Trigonometric Ratios, Review Answers . . . . .8.7Geometry - Second Edition, Extension: Laws of Sines and Cosines, Review Answers8.8Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104105106109111112113114115.Circles, Answer Key9.1Geometry - Second Edition, Parts of Circles and Tangent Lines, Review Answers . . . . . . . .9.2Geometry - Second Edition, Properties of Arcs, Review Answers . . . . . . . . . . . . . . . . .9.3Geometry - Second Edition, Properties of Chords, Review Answers . . . . . . . . . . . . . . . .9.4Geometry - Second Edition, Inscribed Angles, Review Answers . . . . . . . . . . . . . . . . . .9.5Geometry - Second Edition, Angles of Chords, Secants, and Tangents, Review Answers . . . . .9.6Geometry - Second Edition, Segments of Chords, Secants, and Tangents, Review Answers . . .9.7Geometry - Second Edition, Extension: Writing and Graphing the Equations of Circles, ReviewAnswers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.8Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Perimeter and Area, Answer Key10.1Geometry - Second Edition, Triangles and Parallelograms, Review Answers . . . . . .10.2Geometry - Second Edition, Trapezoids, Rhombi, and Kites, Review Answers . . . . .10.3Geometry - Second Edition, Areas of Similar Polygons, Review Answers . . . . . . . .10.4Geometry - Second Edition, Circumference and Arc Length, Review Answers . . . . .10.5Geometry - Second Edition, Areas of Circles and Sectors, Review Answers . . . . . .10.6Geometry - Second Edition, Area and Perimeter of Regular Polygons, Review Answers10.7Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3911 Surface Area and Volume, Answer Key14011.1Geometry - Second Edition, Exploring Solids, Review Answers . . . . . . . . . . . . . . . . . . 141v

ometry - Second Edition, Surface Area of Prisms and Cylinders, Review AnswersGeometry - Second Edition, Surface Area of Pyramids and Cones, Review Answers .Geometry - Second Edition, Volume of Prisms and Cylinders, Review Answers . . .Geometry - Second Edition, Volume of Pyramids and Cones, Review Answers . . . .Geometry - Second Edition, Surface Area and Volume of Spheres, Review Answers .Geometry - Second Edition, Exploring Similar Solids, Review Answers . . . . . . .Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 Rigid Transformations, Answer Key12.1Geometry - Second Edition, Exploring Symmetry, Review Answers . . . . . . .12.2Geometry - Second Edition, Translations and Vectors , Review Answers . . . .12.3Geometry - Second Edition, Reflections, Review Answers . . . . . . . . . . . .12.4Geometry - Second Edition, Rotations, Review Answers . . . . . . . . . . . . .12.5Geometry - Second Edition, Composition of Transformations, Review Answers12.6Geometry - Second Edition, Extension: Tessellations, Review Answers . . . . .12.7Chapter Review Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vi.143144146147148150151.152153155156158162163164

www.ck12.orgChapter 1. Basics of Geometry, Answer KeyC HAPTER1Basics of Geometry,Answer KeyChapter Outline1.1G EOMETRY - S ECOND E DITION , P OINTS , L INES , AND P LANES , R EVIEW A N SWERS1.2G EOMETRY - S ECOND E DITION , S EGMENTS AND D ISTANCE , R EVIEW A NSWERS1.3G EOMETRY - S ECOND E DITION , A NGLES AND M EASUREMENT, R EVIEW A N SWERS1.4G EOMETRY - S ECOND E DITION , M IDPOINTS AND B ISECTORS , R EVIEW A N SWERS1.5G EOMETRY - S ECOND E DITION , A NGLE PAIRS , R EVIEW A NSWERS1.6G EOMETRY - S ECOND E DITION , C LASSIFYING P OLYGONS , R EVIEW A NSWERS1.7G EOMETRY - S ECOND E DITION , C HAPTER R EVIEW A NSWERS1

1.1. Geometry - Second Edition, Points, Lines, and Planes, Review Answerswww.ck12.org1.1 Geometry - Second Edition, Points, Lines,and Planes, Review AnswersFor 1-5, answers will vary. One possible answer for each is included.1.2.3.4. 6. W X, YW , line m, XY and WY .25.

www.ck12.orgChapter 1. Basics of Geometry, Answer Key7. Plane V or plane RST .8. In addition to the pictures to the right, three planes may not intersect at all and can be parallel.9. A 4.25.26.27.28. PQ intersects RS at point Q. AC and AB are coplanar and point D is not. Points E and H are coplanar, but their rays, EF and GH are non-coplanar. IJ , IK, IL, and IM with common endpoint I and J, K, L and M are erAlwaysSometimesNeverAlwaysSometimes#18: By definition, a point does not take up any space, it is only a location. #21: The ray is never read “BA,”the endpoint is always stated first.To make #15 true, they must be three non-collinear points. For #16, the two rays must lie on the same line,which it does not state. For #20, four points could be coplanar, but you only need three points to make a plane,so the fourth point could be in another plane. For #23, theorems can also be proven true by definitions andpreviously proven theorems.The walls, ceiling and floor are all planes. When two of them intersect the intersection is a line (i.e. the ceilingand a wall). When two walls and either the ceiling or the floor intersect the intersection is a point.The spokes on a wheel are segments. They intersect at a point.Cities on a map are points and the distance between them can be found by measuring the segment connectingthe points.29-33.3

1.1. Geometry - Second Edition, Points, Lines, and Planes, Review Answers4www.ck12.org

www.ck12.orgChapter 1. Basics of Geometry, Answer Key1.2 Geometry - Second Edition, Segments andDistance, Review Answers1.2.3.4.5.6.7.8.1.625 in2.875 in3.7 cm8.2 cm2.75 in4.9 cm4.625 in8.7 cm9.10. O would be halfway between L and T , so that LO OT 8 cm11.a.b. TA AQ T Qc. T Q 15 in12.a.b. HM MA HAc. AM 11 cm13. BC 8 cm, BD 25 cm, and CD 17 cm14. FE 8 in, HG 13 in, and FG 17 in15.a.b.c.d.16.17.18.19.20.21.RS 4QS 14TS 8TV 12x 3, HJ 21, JK 12, HK 33x 11, HJ 52, JK 79, HK 131x 1, HJ 2 31 , JK 5 32 , HK 8x 17, HJ 27, JK 153, KH 180x 16, HJ 7, JK 15, KH 22One possible answer.5

1.2. Geometry - Second Edition, Segments and Distance, Review Answerswww.ck12.org 7 ( 6) 13 3 2 5 0 ( 9) 9 4 1 5Answers vary, but hopefully most students found their heights to be between 7 and 8 heads.Answers should include some reference to the idea that multiplying and dividing by ten (according to theprefixes) is much easier than keeping track of 12 inches in a ft, 3 ft in a yard, 5280 ft in a mile, etc.28.