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DG4PSA 894 fm qxd 4 28 08 7 53 PM Page ii, Teacher s Materials Project Editor Elizabeth DeCarli. Project Administrator Brady Golden, Coordinating Writer Jennifer North Morris. Contributors David Rasmussen Ralph Bothe Judy Hicks Michael Serra. Accuracy Checker Dudley Brooks, Production Editor Holly Rudelitsch. Copyeditor Jill Pellarin, Editorial Production Manager Christine Osborne. Production Supervisor Ann Rothenbuhler, Production Coordinator Jennifer Young.

Text Designers Jenny Somerville Garry Harman, Composition Technical Art Prepress ICC Macmillan Inc . Cover Designer Jill Kongabel, Printer Data Reproductions. Textbook Product Manager James Ryan, Executive Editor Casey FitzSimons. Publisher Steven Rasmussen, 2008 by Key Curriculum Press All rights reserved . Cover Photo Credits Background image Doug Wilson Westlight Corbis . Construction site image Sonda Dawes The Image Works All other images . Ken Karp Photography , Limited Reproduction Permission.

The publisher grants the teacher whose school has adopted Discovering Geometry . and who has received Discovering Geometry An Investigative Approach Practice. Your 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 Unauthorized. copying of Discovering Geometry An Investigative Approach Practice Your Skills. with Answers constitutes copyright infringement and is a violation of federal law . Key Curriculum Press is a registered trademark of Key Curriculum Press . All registered trademarks and trademarks in this book are the property of. their respective holders , Key Curriculum Press, 1150 65th Street. Emeryville CA 94608, 510 595 7000, editorial keypress com. www keypress com, Printed in the United States of America. 10 9 8 7 6 5 4 3 2 13 12 11 10 09 08 ISBN 978 1 55953 894 7. DG4PSA 894 fm qxd 11 1 06 11 16 AM Page iii, Introduction vi. Lesson 1 1 Building Blocks of Geometry 1, Lesson 1 2 Poolroom Math 2.

Lesson 1 3 What s a Widget 3, Lesson 1 4 Polygons 4. Lesson 1 5 Triangles 5, Lesson 1 6 Special Quadrilaterals 6. Lesson 1 7 Circles 7, Lesson 1 8 Space Geometry 8. Lesson 1 9 A Picture Is Worth a Thousand Words 9, Lesson 2 1 Inductive Reasoning 10. Lesson 2 2 Finding the nth Term 11, Lesson 2 3 Mathematical Modeling 12.

Lesson 2 4 Deductive Reasoning 13, Lesson 2 5 Angle Relationships 14. Lesson 2 6 Special Angles on Parallel Lines 15, Lesson 3 1 Duplicating Segments and Angles 16. Lesson 3 2 Constructing Perpendicular Bisectors 17. Lesson 3 3 Constructing Perpendiculars to a Line 18. Lesson 3 4 Constructing Angle Bisectors 19, Lesson 3 5 Constructing Parallel Lines 20. Lesson 3 6 Construction Problems 21, Lesson 3 7 Constructing Points of Concurrency 22. Lesson 3 8 The Centroid 23, Lesson 4 1 Triangle Sum Conjecture 24.

Lesson 4 2 Properties of Isosceles Triangles 25, Lesson 4 3 Triangle Inequalities 26. Lesson 4 4 Are There Congruence Shortcuts 27, Lesson 4 5 Are There Other Congruence Shortcuts 28. Lesson 4 6 Corresponding Parts of Congruent Triangles 29. Lesson 4 7 Flowchart Thinking 30, Lesson 4 8 Proving Special Triangle Conjectures 31. DG4PSA 894 fm qxd 11 1 06 11 16 AM Page iv, Lesson 5 1 Polygon Sum Conjecture 32. Lesson 5 2 Exterior Angles of a Polygon 33, Lesson 5 3 Kite and Trapezoid Properties 34.

Lesson 5 4 Properties of Midsegments 35, Lesson 5 5 Properties of Parallelograms 36. Lesson 5 6 Properties of Special Parallelograms 37. Lesson 5 7 Proving Quadrilateral Properties 38, Lesson 6 1 Tangent Properties 39. Lesson 6 2 Chord Properties 40, Lesson 6 3 Arcs and Angles 41. Lesson 6 4 Proving Circle Conjectures 42, Lesson 6 5 The Circumference Diameter Ratio 43. Lesson 6 6 Around the World 44, Lesson 6 7 Arc Length 45.

Exploration Intersecting Secants Tangents and Chords 46. Lesson 7 1 Transformations and Symmetry 47, Lesson 7 2 Properties of Isometries 48. Lesson 7 3 Compositions of Transformations 49, Lesson 7 4 Tessellations with Regular Polygons 50. Lessons 7 5 7 8 Tessellations 51, Lesson 8 1 Areas of Rectangles and Parallelograms 52. Lesson 8 2 Areas of Triangles Trapezoids and Kites 53. Lesson 8 3 Area Problems 54, Lesson 8 4 Areas of Regular Polygons 55. Lesson 8 5 Areas of Circles 56, Lesson 8 6 Any Way You Slice It 57.

Lesson 8 7 Surface Area 58, Lesson 9 1 The Theorem of Pythagoras 59. Lesson 9 2 The Converse of the Pythagorean Theorem 60. Lesson 9 3 Two Special Right Triangles 61, Lesson 9 4 Story Problems 62. Lesson 9 5 Distance in Coordinate Geometry 63, Lesson 9 6 Circles and the Pythagorean Theorem 64. DG4PSA 894 fm qxd 11 1 06 11 16 AM Page v, Chapter 10. Lesson 10 1 The Geometry of Solids 65, Lesson 10 2 Volume of Prisms and Cylinders 66.

Lesson 10 3 Volume of Pyramids and Cones 67, Lesson 10 4 Volume Problems 68. Lesson 10 5 Displacement and Density 69, Lesson 10 6 Volume of a Sphere 70. Lesson 10 7 Surface Area of a Sphere 71, Chapter 11. Lesson 11 1 Similar Polygons 72, Lesson 11 2 Similar Triangles 73. Lesson 11 3 Indirect Measurement with Similar Triangles 74. Lesson 11 4 Corresponding Parts of Similar Triangles 75. Lesson 11 5 Proportions with Area 76, Lesson 11 6 Proportions with Volume 77.

Lesson 11 7 Proportional Segments Between Parallel Lines 78. Chapter 12, Lesson 12 1 Trigonometric Ratios 79, Lesson 12 2 Problem Solving with Right Triangles 80. Lesson 12 3 The Law of Sines 81, Lesson 12 4 The Law of Cosines 82. Lesson 12 5 Problem Solving with Trigonometry 83, Chapter 13. Lesson 13 1 The Premises of Geometry 84, Lesson 13 2 Planning a Geometry Proof 85. Lesson 13 3 Triangle Proofs 86, Lesson 13 4 Quadrilateral Proofs 87.

Lesson 13 5 Indirect Proof 88, Lesson 13 6 Circle Proofs 89. Lesson 13 7 Similarity Proofs 90, Answers 91, DG4PSA 894 fm qxd 11 1 06 11 16 AM Page vi. Introduction, The author and editors of Discovering Geometry An Investigative Approach are. aware of the importance of students developing geometry skills along with. acquiring concepts through investigation The student book includes many. skill based exercises These Practice Your Skills worksheets provide problems. similar to the introductory exercises in each lesson of Discovering Geometry Like. those exercises these worksheets allow students to practice and reinforce the. important procedures and skills developed in the lessons Some of these problems. provide non contextual skills practice Others give students an opportunity to. apply geometry concepts in fairly simple straightforward contexts Some are more. complex problems that are broken down into small steps . You might assign the Practice Your Skills worksheet for every lesson or only for. those lessons your students find particularly difficult Or you may wish to. assign the worksheets on an individual basis only to those students who need. extra help One worksheet has been provided for nearly every lesson There are. no worksheets for Chapter 0 and the optional tessellation lessons have been. combined into two worksheets To save you the time and expense of copying. pages you can give students the inexpensive Practice Your Skills Student Workbook . which does not have answers Though the copyright allows you to copy pages. from Practice Your Skills with Answers for use with your students the consumable. Practice Your Skills Student Workbook should not be copied Students parents and. mentors can also download the student worksheets from www keymath com . DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 1, Lesson 1 1 Building Blocks of Geometry. Name Period Date, For Exercises 1 7 complete each statement PS P Q.

N S, is , 1 The midpoint of PQ, 2 NQ , is , 3 Another name for NS. 4 S is the of SQ, 5 P is the midpoint of , , is , 7 Another name for SN. 8 Name all pairs of congruent segments in KLMN Use the N. congruence symbol to write your answer 8 cm, K M, D has coordinates 6 1 Find the. 9 M 4 8 is the midpoint of DE L, coordinates of E . For Exercises 10 and 11 use a ruler to draw each figure Label the. figure and mark the congruent parts , 10 AB with M as the midpoint and CD.

11 AB C is the midpoint of AB, of both AB AB 6 4 cm is the. AC 1 5 cm D not on AB, and CD 4 0 cm A B and C are . midpoint of AE with AD 2BC , not collinear , 12 Sketch six points A B C D E and F no 13 In the figure below B C H E is a set of. three of which are collinear Name the lines four coplanar points Name two other sets. defined by these points How many lines of four coplanar points How many sets of. are there four coplanar points are there , B C, A D. F G, E H, Discovering Geometry Practice Your Skills CHAPTER 1 1.

2008 Key Curriculum Press, DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 2. Lesson 1 2 Poolroom Math, Name Period Date, For Exercises 1 5 use the figure at right to complete B. each statement , 1 A is the of BAE C, is the of BAE . 2 AD A, is a of DAE , 4 If m BAC 42 then m CAE , 5 DAB . For Exercises 6 9 use your protractor to find the measure of. each angle to the nearest degree , 6 m PRO 7 m ORT R T A.

8 m O 9 m RTO, For Exercises 10 12 use your protractor to draw and then label. each angle with the given measure , 10 m MNO 15 11 m RIG 90 12 m z 160 . For Exercises 13 15 find the measure of the angle formed by the. hands at each time 11, 10 2, 13 3 00 14 4 00 15 3 30. 9 3, 8 4, 7 5, For Exercises 16 and 17 mark each figure with all the given information 6. 16 m ADB 90 AD BD DAB DBA, A D C, 17 m RPQ 90 QR TZ RT QZ Q T.

R T, Q P Z, 2 CHAPTER 1 Discovering Geometry Practice Your Skills. 2008 Key Curriculum Press, DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 3. Lesson 1 3 What s a Widget , Name Period Date, For Exercises 1 9 match each term with one of the items a to i below . a 2 b c , d e f , g h P, 1 Vertical angles 2 Obtuse angle. 3 Right angle 4 Complementary angles, 5 Congruent angles 6 Linear pair of angles.

7 Bisected angle 8 Perpendicular lines, 9 Congruent segments. 10 If m P 13 m Q 77 and Q and R are complementary what. can you conclude about P and R Explain your reasoning . For Exercises 11 13 sketch label and mark a figure showing. each property , 11 1 2 2 3 12 PQ , PR 13 BAC XAY CX BC. Discovering Geometry Practice Your Skills CHAPTER 1 3. 2008 Key Curriculum Press, DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 4. Lesson 1 4 Polygons, Name Period Date, For Exercises 1 8 complete the table . Polygon name Number of sides Number of diagonals, 1 Triangle.

2 2, 3 5, 4 Hexagon, 5 Heptagon, 6 8, 7 35, 8 12, For Exercises 9 and 10 sketch and label each figure Mark the congruences . 9 Concave pentagon PENTA with external 10 Equilateral quadrilateral QUAD with. diagonal ET PE, Q U , For Exercises 11 14 sketch and use hexagon ABCDEF . 11 Name the diagonals from A , 12 Name a pair of consecutive sides . 13 Name a pair of consecutive angles , 14 Name a pair of non intersecting diagonals . For Exercises 15 18 use the figures at right , MNOPQ RSTUV T.

15 m N 61 U, 16 VR Q, P 8 4 82 58 , 17 m P S R, 18 ON M. 19 The perimeter of a regular pentagon is 31 cm Find the length of. each side , 4 CHAPTER 1 Discovering Geometry Practice Your Skills. 2008 Key Curriculum Press, DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 5. Lesson 1 5 Triangles, Name Period Date, For Exercises 1 5 use the figure at right Name a pair of. 1 Parallel segments A B, 2 Perpendicular segments.

C D E F, 3 Congruent segments, 4 Supplementary angles. 5 Linear angles G H I, For Exercises 6 and 7 sketch label and mark each figure . 6 Isosceles obtuse triangle TRI with vertex angle T . 7 Scalene right triangle SCA with midpoints L M and N on SC . respectively , For Exercises 8 and 9 use your geometry tools to draw each figure . 8 Acute isosceles triangle ACD with vertex 9 Scalene right triangle RGH . angle A measuring 40 , For Exercises 10 12 use the graph at right y. 10 Locate F so that ABF is a right triangle , 11 Locate D so that ABD is an isosceles triangle .

12 Locate G so that ABG is scalene and not a right triangle A 0 0 B 8 0 . Discovering Geometry Practice Your Skills CHAPTER 1 5. 2008 Key Curriculum Press, DG4PSA 894 01 qxd 11 1 06 1 26 PM Page 6. Lesson 1 6 Special Quadrilaterals, Name Period Date. For Exercises 1 6 sketch label and mark each figure . 1 Parallelogram PGRA 2 Square SQRE, 3 Rhombus RHOM with acute H AP. 4 Trapezoid TRAP with TR RE, and P E and A collinear . 5 Kite KITE with EK KI and obtuse K 6 Rectangle RANG with perimeter 2a 4b. For Exercises 7 10 name each polygon in the figure Assume that H J. the grid is square , G I, 7 Square 8 Parallelogram.

D F, 9 Rhombus 10 Kite A C, For Exercises 11 13 use the graph at right y. 11 Locate D so that ABCD is a rectangle , 12 Locate E so that ABCE is a trapezoid . 13 Locate G so that points A B C and G A 0 0 B 8 0 . and who has received Discovering Geometry An Investigative Approach Practice Your 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 Unauthorized copying ofDiscovering Geometry An Investigative Approach Practice Your Skills

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