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1 NEW YORK GEOMETRY TABLE OF CONTENTS CHAPTER 1 POINTS, LINES, & PLANES {G.G.21, G.G.27} TOPIC A: Concepts Relating to Points, Lines, and Planes PART 1: Basic Concepts and Definitions...1 PART 2: Concepts Involving Definitions...2 PART 3: Concept of a Postulate and Theorem...3 TOPIC B: Separation of Points and Collinear Points...4 TOPIC C: Lines and Line Segments...5 TOPIC D: Basic Concepts of Intersecting Lines and Angles PART 1: Measure of Angles...6 PART 2: Identification of Angle Types and Relationships...7 PART 3: Complement of an Angle...8 PART 4: Supplement of an Angle...8 PART 5: Angle Complement and Supplement Word Problems...9 PART 6: Relationships Between Angles (True/False)...10 PART 7: Relationship Between Angles (Intersecting and Perpendicular Lines)...10 TOPIC E: Angle and Line Segment Relationships in Triangles...12 TOPIC F: Concurrent Lines in a Triangle...15 TOPIC G: Proofs Based on Triangles and Lines...16 CHAPTER 2 CONGRUENT TRIANGLES {G.G.27-G.G.29} TOPIC A: Identifying Congruent Angles and Sides...23 TOPIC B: Indicating the Reason Two Triangles are Congruent...24 TOPIC C: Congruent Triangle Proofs PART 1: Separate Triangles...28 PART 2: Combined Triangles...29 PART 3: Corresponding Parts of Congruent Triangles Congruent...33 PART 4: Overlapping Triangles...36 PART 5: Given Two Pairs of Congruent Triangles...38 CHAPTER 3 ISOSCELES & EQUILATERAL TRIANGLES {G.G.27, G.G.31} TOPIC A: General Problems (True/False)...41 TOPIC B: Finding the Value of a Side or Angle...41 TOPIC C: Perpendicular Bisectors...44 TOPIC D: Auxiliary Sets of Points...45 TOPIC E: Isosceles and Equilateral Triangle Proofs...45 CHAPTER 4 LOGIC & INDIRECT PROOFS {G.G.24- G.G.26} TOPIC A: Negation of a Statement...55 TOPIC B: Truth Value of a Statement...56 TOPIC C: Special Conditional Statements PART 1: Converse...63 PART 2: Inverse...65 PART 3: Contrapositive...66 PART 4: Logically Equivalent Statements...66 PART 5: Combination Problems...68 TOPIC D: Indirect Proofs...69 CHAPTER 5 INEQUALITIES IN ONE TRIANGLE {G.G.32- G.G.34} TOPIC A: Inequality Postulates...73 TOPIC B: Relationships Between Interior and Exterior Angles of Triangles...73 TOPIC C: Qualitative Evaluation of the Dimensions of a Triangle...74 TOPIC D: Drawing Triangles to Specified Conditions...77 TOPIC E: Constraints on Three Sides of a Triangle...78

2 TOPIC F: Inequality Proofs PART 1: Supplying Missing Reasons...80 PART 2: Two-Column Proofs...82 PART 3: Emphasizing Interior and Exterior Angles...83 PART 4: Angle Inequalities...84 PART 5: Side Inequalities...84 CHAPTER 6 PARALLEL LINES {G.G.35} TOPIC A: Recognizing Angle Relationships (Two Lines Cut by a Transversal)...89 TOPIC B: Lines and Angles Associated with a Transversal...90 TOPIC C: Properties of Parallel Lines...92 TOPIC D: Parallel Line Proofs PART 1: Proving Lines are Parallel PART 2: Proofs Using Parallel Lines CHAPTER 7 QUADRILATRALS {G.G.38-G.G.41} TOPIC A: Parallelograms PART 1: Side and Angle Relationships PART 2: Finding the Measure of Diagonals PART 3: Finding the Measure of Sides PART 4: Finding the Measure of Angles PART 5: Congruency Proofs TOPIC B: Proving that a Quadrilateral is a Parallelogram TOPIC C: Squares, Rectangles, and Rhombuses PART 1: Squares PART 2: Rectangles PART 3: Rhombuses PART 4: Summary Properties of Parallelograms TOPIC D: Trapezoids CHAPTER 8 SIMILARITY {G.G.42- G.G.47} TOPIC A: Ratio and Proportion TOPIC B: Similar Polygons TOPIC C: Midpoints of Triangles and Parallel Lines PART 1: Finding the Value of Angles and Sides PART 2: Perimeter TOPIC D: Triangle Proportionality TOPIC E: Indicating the Reason Two Triangles are Similar TOPIC F: Similar Triangle Proofs TOPIC G: Perimeters and Areas of Similar Polygons TOPIC H: Altitude Drawn to the Hypotenuse in a Right Triangle TOPIC I: Medians of a Triangle TOPIC J: Using Proportions in Similar Polygons CHAPTER 9 THE RIGHT TRIANGLE {G.G.48} TOPIC A: The Pythagorean Theorem PART 1: Lengths of Sides of a Right Triangle PART 2: Converse of the Pythagorean Theorem TOPIC B: Special Right Triangles PART 1: The Isosceles Right Triangle ( ) PART 2: The Triangle CHAPTER 10 LOCUS {G.G.22-G.G.23} TOPIC A: Locus of Points PART 1: Describing a Locus of Points PART 2: Drawing a Locus of Points TOPIC B: Intersection of Loci TOPIC C: Locus in Coordinate Geometry PART 1: Equation of the Locus of Points PART 2: Intersection of Loci...191

3 CHAPTER 11 CIRCLES {G.G.49, G.G.53} TOPIC A: Fundamental Relationships TOPIC B: Chords, Secants, and Tangents PART 1: Length of Segments Section a: Given Chords and Radius or Diameter Section b: Given Intersecting Chords Section c: Given Tangents and Secants Section d: Given Multiple Secants Section e: Given Multiple Tangents PART 2: Measure of Angles and Arcs Section a: Measures of Central Angles and Intercepted Arcs Section b: Measures of Inscribed Angles and Intercepted Arcs Section c: Relationship of Central Angle to Inscribed Angle Measures Section d: Measures of Angles and Arcs Formed by Internal Intersections of Tangents, Chords, or Secants Section e: Measures of Angles and Arcs Formed by External Intersections of Tangents and Secants Section f: Multipart Questions TOPIC C: Length of an Arc or Segment TOPIC D: Tangent Circles TOPIC E: Circumference of a Circle TOPIC F: Areas of Circles, Sectors, and Segments PART 1: Finding Area of a Circle Given Radius, Diameter, or Circumference PART 2: Finding Radius or Circumference Given Area PART 3: Finding Area of an Inscribed or Circumscribed Circle PART 4: Finding Area of a Sector PART 5: Finding Area of Shaded Regions PART 6: Multipart Questions TOPIC G: Ratios in Circles TOPIC H: Circle Proofs CHAPTER 12 POLYGONS {G.G.30, G.G.36-G.G.37} TOPIC A: Diagonals in a Polygon TOPIC B: Interior and Exterior Angles of Polygons PART 1: Angle Measures of a Triangle Section a: Sum of Interior Angles Section b: Exterior Angle Measure PART 2: Angle Measures of a Polygon Section a: Sum of Interior Angles Section b: Exterior Angle Measure Section c: Angles and Sides of Regular Polygons TOPIC C: Perimeter of Polygons TOPIC D: Regular Polygons PART 1: Regular Polygons (True/False) PART 2: Central Angles PART 3: Apothem and Area of Regular Polygons Section a: Relationship of Apothem Measure to Side Measure Section b: Inscribed and Circumscribed Regular Polygons Section c: Area of Regular Polygons CHAPTER 13 COORDINATE GEOMETRY {G.G.62-G.G.69, G.G.71-G.G.74} TOPIC A: Plotting Coordinate Points PART 1: Coordinate Definitions PART 2: Quadrants PART 3: Coordinates of a Point TOPIC B: Finding Area and Perimeter Using Coordinates TOPIC C: Midpoint of a Segment PART 1: Finding the Midpoint of a Segment PART 2: Finding the Endpoint of a Segment (Given the Midpoint)...299

4 PART 3: Intersection of Diagonals in a Parallelogram TOPIC D: Slope of a Line PART 1: Slope Definitions PART 2: Finding the Slope of a Line (Given Points) PART 3: Finding a Point (Given the Slope) PART 4: Collinearity of Points PART 5: Slopes of Parallel and Perpendicular Lines TOPIC E: Distance Between Two Points TOPIC F: Equation of a Line PART 1: Determining Slope and Y-intercept from a Linear Equation PART 2: Writing an Equation of a Line (Given Slope and Y-intercept) PART 3: Writing an Equation of a Line (Given Slope and a Point) PART 4: Writing an Equation of a Line (Given Two Points) PART 5: Equations of Parallel and Perpendicular Lines Section a: Parallel Lines Section b: Perpendicular Lines TOPIC G: Graphs of Linear Equations TOPIC H: Equation of a Circle PART 1: Determining the Equation of a Circle PART 2: Determining the Center and Radius (Given the Equation of a Circle) PART 3: Graphing Circles PART 4: Equation of a Sphere TOPIC I: Systems of Equations PART 1: Systems of Linear Equations PART 2: Systems of Linear and Parabolic Equations PART 3: Systems of Circles and Linear Equations TOPIC J: Coordinate Proofs (Specific Coordinates) TOPIC K: Proofs of Theorems (Variable Coordinates) CHAPTER 14 TRANSFORMATION GEOMETRY {G.G.54-G.G.61} TOPIC A: Congruency Transformations PART 1: Isometries Section a: Line Reflections Section b: Point Reflections Section c: Rotations Section d: Translations Section e: Glide Reflections PART 2: Properties of Isometries PART 3: Justification of Geometric Relationships TOPIC B: Similarity Transformations PART 1: Properties of Similarities PART 2: Dilations PART 3: Composition of Dilations and Isometries CHAPTER 15 SPACIAL GEOMETRY {G.G.1-G.G.15} TOPIC A: Perpendicular and Parallel Lines and Planes TOPIC B: Properties and Formulas of Geometric Solids TOPIC C: Area and Volume of Geometric Solids PART 1: Prisms: Section a: Lateral Surface Area Section b: Total Surface Area Section c: Volume PART 2: Pyramids Section a: Lateral Surface Area Section b: Total Surface Area Section c: Volume PART 3: Cylinders Section a: Lateral Surface Area Section b: Total Surface Area...402

5 Section c: Volume PART 4: Right Circular Cones Section a: Lateral Surface Area Section b: Total Surface Area Section c: Volume PART 5: Spheres Section a: Surface Area Section b: Volume PART 6: Composite Solids Section a: Surface Area Section b: Volume TOPIC D: Effect of Changing Dimensions on Surface Area and Volume PART 1: Surface Area PART 2: Volume Section a: Cubes, Rectangular Prisms, and Pyramids Section b: Cylinders, Cones, and Spheres CHAPTER 16 CONSTRUCTIONS {G.G.17-G.G.20} TOPIC A: Construction Using a Straightedge, Compass, and/or Protractor PART 1: Copying, Constructing, and Dividing Line Segments PART 2: Constructing and Copying Angle Measures PART 3: Constructing Similar Figures PART 4: Constructing Angle Bisectors PART 5: Locating the Midpoint of a Segment PART 6: Constructing Perpendicular and Parallel Lines PART 7: Constructing Altitudes, Medians, and Perpendicular Bisectors PART 8: Constructing Geometric Figures Having Specific Conditions PART 9: Circle Constructions TOPIC B: Constructions Involving Concurring Lines of a Triangle PART 1: Constructing the Circumcenter (Concurrent Perpendicular Bisectors) and Circumscribing Figures PART 2: Constructing the Incenter (Concurrent Angle Bisectors) and Inscribing Circles PART 3: Constructing the Centroid (Concurrent Medians) PART 4: Constructing the Orthocenter (Concurrent Altitudes) TOPIC C: Constructions Involving Locus TOPIC D: Construction Proofs APPENDIX HOW TO ADD MATH GRIDS & TABLES TO AN EXAM...469

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