Discovering Geometry: An Investigative Approach

by Rasmussen, David; Bothe, Ralph; Hicks, Judy; Serra, Michael

• ISBN13: 9781559535953
• ISBN10: 1559535954
• Edition: Student
• Format: Paperback
• Copyright: 2003-01-31
• Publisher: Key Curriculum Pr

Table of Contents

Introduction	vii
Chapter 1
Lesson 1.1: Building Blocks of Geometry	1	(1)
Lesson 1.2: Poolroom Math	2	(1)
Lesson 1.3: What's a Widget?	3	(1)
Lesson 1.4: Polygons	4	(1)
Lesson 1.5: Triangles and Special Quadrilaterals	5	(1)
Lesson 1.6: Circles	6	(1)
Lesson 1.7: A Picture Is Worth a Thousand Words	7	(1)
Lesson 1.8: Space Geometry	8	(1)
Chapter 2
Lesson 2.1: Inductive Reasoning	9	(1)
Lesson 2.2: Deductive Reasoning	10	(1)
Lesson 2.3: Finding the nth Term	11	(1)
Lesson 2.4: Mathematical Modeling	12	(1)
Lesson 2.5: Angle Relationships	13	(1)
Lesson 2.6: Special Angles on Parallel Lines	14	(1)
Chapter 3
Lesson 3.1: Duplicating Segments and Angles	15	(1)
Lesson 3.2: Constructing Perpendicular Bisectors	16	(1)
Lesson 3.3: Constructing Perpendiculars to a Line	17	(1)
Lesson 3.4: Constructing Angle Bisectors	18	(1)
Lesson 3.5: Constructing Parallel Lines	19	(1)
Lesson 3.6: Construction Problems	20	(1)
Lesson 3.7: Constructing Points of Concurrency	21	(1)
Lesson 3.8: The Centroid	22	(1)
Chapter 4
Lesson 4.1: Triangle Sum Conjecture	23	(1)
Lesson 4.2: Properties of Special Triangles	24	(1)
Lesson 4.3: Triangle Inequalities	25	(1)
Lesson 4.4: Are There Congruence Shortcuts?	26	(1)
Lesson 4.5: Are There Other Congruence Shortcuts?	27	(1)
Lesson 4.6: Corresponding Parts of Congruent Triangles	28	(1)
Lesson 4.7: Flowchart Thinking	29	(1)
Lesson 4.8: Proving Isosceles Triangle Conjectures	30	(1)
Chapter 5
Lesson 5.1: Polygon Sum Conjecture	31	(1)
Lesson 5.2: Exterior Angles of a Polygon	32	(1)
Lesson 5.3: Kite and Trapezoid Properties	33	(1)
Lesson 5.4: Properties of Midsegments	34	(1)
Lesson 5.5: Properties of Parallelograms	35	(1)
Lesson 5.6: Properties of Special Parallelograms	36	(1)
Lesson 5.7: Proving Quadrilateral Properties	37	(1)
Chapter 6
Lesson 6.1: Chord Properties	38	(1)
Lesson 6.2: Tangent Properties	39	(1)
Lesson 6.3: Arcs and Angles	40	(1)
Lesson 6.4: Proving Circle Conjectures	41	(1)
Lesson 6.5: The Circumference/Diameter Ratio	42	(1)
Lesson 6.6: Around the World	43	(1)
Lesson 6.7: Arc Length	44	(1)
Chapter 7
Lesson 7.1: Transformations and Symmetry	45	(1)
Lesson 7.2: Properties of Isometries	46	(1)
Lesson 7.3: Compositions of Transformations	47	(1)
Lessons 7.4--7.8: Tessellations	48	(1)
Chapter 8
Lesson 8.1: Areas of Rectangles and Parallelograms	49	(1)
Lesson 8.2: Areas of Triangles, Trapezoids, and Kites	50	(1)
Lesson 8.3: Area Problems	51	(1)
Lesson 8.4: Areas of Regular Polygons	52	(1)
Lesson 8.5: Areas of Circles	53	(1)
Lesson 8.6: Any Way You Slice It	54	(1)
Lesson 8.7: Surface Area	55	(1)
Chapter 9
Lesson 9.1: The Theorem of Pythagoras	56	(1)
Lesson 9.2: The Converse of the Pythagorean Theorem	57	(1)
Lesson 9.3: Two Special Right Triangles	58	(1)
Lesson 9.4: Story Problems	59	(1)
Lesson 9.5: Distance in Coordinate Geometry	60	(1)
Lesson 9.6: Circles and the Pythagorean Theorem	61	(1)
Chapter 10
Lesson 10.1: The Geometry of Solids	62	(1)
Lesson 10.2: Volume of Prisms and Cylinders	63	(1)
Lesson 10.3: Volume of Pyramids and Cones	64	(1)
Lesson 10.4: Volume Problems	65	(1)
Lesson 10.5: Displacement and Density	66	(1)
Lesson 10.6: Volume of a Sphere	67	(1)
Lesson 10.7: Surface Area of a Sphere	68	(1)
Chapter 11
Lesson 11.1: Similar Polygons	69	(1)
Lesson 11.2: Similar Triangles	70	(1)
Lesson 11.3: Indirect Measurement with Similar Triangles	71	(1)
Lesson 11.4: Corresponding Parts of Similar Triangles	72	(1)
Lesson 11.5: Proportions with Area and Volume	73	(1)
Lesson 11.6: Proportional Segments Between Parallel Lines	74	(1)
Chapter 12
Lesson 12.1: Trigonometric Ratios	75	(1)
Lesson 12.2: Problem Solving with Right Triangles	76	(1)
Lesson 12.3: The Law of Sines	77	(1)
Lesson 12.4: The Law of Cosines	78	(1)
Lesson 12.5: Problem Solving with Trigonometry	79	(1)
Chapter 13
Lesson 13.1: The Premises of Geometry	80	(1)
Lesson 13.2: Planning a Geometry Proof	81	(1)
Lesson 13.3: Triangle Proofs	82	(1)
Lesson 13.4: Quadrilateral Proofs	83	(1)
Lesson 13.5: Indirect Proof	84	(1)
Lesson 13.6: Circle Proofs	85	(1)
Lesson 13.7: Similarity Proofs	86