Standard Geometry - McDougal Littell Textbook. Web-based Practice:

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1 Geometry Logic and Proofs Strand G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and theorems). Understand the differences among supporting evidence, counterexamples, and actual proofs. Understand the differences among supporting evidence, counterexamples, and actual proofs. Understand the structure of an axiomatic system. Sec. 1.1 Identify Points, Lines and Planes Challenge problem p. 8 #46 pdf Sec. 1.2 Segments and Congruence Challenge problem p. 14 #36 Sec. 1.3 Use Midpoint and Distance Formulas Mixed Review p. 23 #1-8 Sec. 2.1 Use Inductive Reasoning Problem Solving p. 77 #34, 35 Sec. 2.2 Analyze Conditional Statements Problem Solving P. 84 #35

2 Sec. 1.1 Identify Points, Lines and Planes H.O.T. problems p. 11 #58, 59 Sec. 1.2 Linear Measures H.O.T. problems p. 20 #38, 40 Sec. 1.4 Angle Measure H.O.T. problems #52 Sec. 2.1 Inductive Reasoning and Conjecture Real-World problems p. 95 # 47, 49 Sec. 2.3 Conditional Statements Real-World problems p. 112 #59, 60, 61 H.O.T. problem p. 112 #63, 65 Mathematics Pacing Resource Document

3 Geometry Logic and Proofs Strand G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric notation. Define angle, circle, perpendicular line, parallel line, and line segment in terms of point, line and plane. Use proper geometric notation. Sec. 1.5 Describe Angle Pair Relationships Problem Solving p. 40 #53, 54 New Jersey Center for Learning and Teaching: Geometry: Points, lines, angles, planes presentation and construction worksheet. Sec. 2.1 Use Inductive Reasoning Sec. 2.2 Analyze Conditional Statements Sec. 2.3 Deductive reasoning Sec. 2.4 Use Postulates and Diagrams Problem Solving problems p. 101 #34-39 Sec. 2.5 Reason Using Properties of Algebra Problem Solving problem p. 110 #33 Sec. 2.6 How Proofs are used in Mathematics: Angles and Segments Problem Solving problem p. 119 #29

4 Sec. 2.7 Prove Angle Pair Relationship Problem Solving p. 129 #36, 37 Sec. 1.5 Angle Relationships H.O.T. problem p. 53 #51 Sec. 2.1 Inductive Reasoning and Conjecture P. 95 #48 Sec. 2.5 Postulates and Paragraph Proofs Real-World problem p. 130 #42 Sec. 2.6 Algebraic Proofs Challenge problem p. 140 #37 Sec. 2.7 Proving Segments Relationships H.O.T. problem p. 147 #17 Sec. 2.8 Proving Angle Relationships H.O.T. problem p. 156 #32

5 Geometry Logic and Proofs Strand G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional ( if then ) and biconditional ( if and only if ) statements. Understand and use the converse, inverse, contrapositive of conditional ( if then } and bi-conditional ( if and only if } statements. Sec. 2.2 Analyze Conditional Statements Problem Solving problem p. 84 #35 Sec. 2.3 Deductive Reasoning p. 92 #24 Persuasive Letter Sec. 2.3 Conditional Statements Problem Solving p. 112 #59-61, 63, 65 Sec. 2.4 Deductive Reasoning H.O.T. problem p. 122 #45

6 Geometry Logic and Proofs Strand G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs, and flow charts formats. Develop geometric proofs using direct and indirect proofs. Develop geometric proofs using contradiction and proofs involving coordinate geometry. Develop geometric proofs using a two-column format, a paragraph format and a flow chart format. Sec. 2.4 Use Postulates and Diagrams p. 101 #34-39 Sec. 2.5 Reason Using Properties of Algebra p. 110 #33 feromax.com/cgi-bin/proveit.pl If need be goggle search geometric proofs and look for ProveIt! Two-Column Proofs Practice Tool Persuasive Letter Sec. 2.6 How Proofs are used in Mathematics: Angles and Segments p. 119 #29 Sec. 2.7 Prove Angle Pair Relationships p. 129 #36, 37 Sec. 2.5 Postulates and Paragraph Proofs p. 130

7 Sec. 2.6 Algebraic Proofs p. 140 #37 Sec. 2.7 Proving Segments Relationship p. 147 #17 Sec. 2.8 Proving Angle Relationship p. 156 #32 Sec. 3.5 Proving Lines Parallel H.O.T. p. 211 #37

8 Geometry Points, Lines, Angles, and Planes Strand G.PL.1: Identify, justify, and apply properties of planes. Identify properties of planes. Justify properties of planes. Apply properties of planes. Not Covered in Quarter One Sec. 3.1 Parallel Lines and Transversals H.O.T. problem p. 175 #47 New Jersey Center for Teaching and Learning: Geometry - Points, lines, and Planes Presentation - Points, lines, and Planes Worksheet Khan Academy: Geometry - Introduction to Euclidean Geometry: Specifying planes in three dimensions. Virtual Nerd: Geometry -Fundamentals of Geometry: What is a plane

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10 Geometry Points, Lines, Angles, and Planes G.PL.3: Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are supplementary; and points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment. Prove and apply the theorem about vertical angles are congruent. Prove and apply the theorem about alternate interior angles are congruent when parallel lines are cut by a transversal. Prove and apply the theorem about alternate exterior angles are congruent when parallel lines are cut by a transversal. Prove and apply the theorem about corresponding angles are congruent when parallel lines are cut by a transversal. Prove and apply the theorem about same side angles are supplementary when parallel lines are cut by a transversal. Prove and apply the theorem about points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment. Not Covered in Quarter One Sec. 3.2 Angles and Parallel Lines H.O.T. problem p. 183 #42 New Jersey Center for Teaching and Learning: Geometry - Parallel and Perpendicular Lines Presentation Khan Academy: Geometry - Angles and Intersecting Lines: Angles between Intersecting and Parallel Lines Virtual Nerd: Geometry -Fundamentals of Geometry: Angle Pair Relationships

11 Geometry Points, Lines, Angles, and Planes Strand G.PL.4: Know that parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Determine if a pair of lines are parallel, perpendicular, or neither by comparing the slopes in coordinate graphs and in equations. Find the equation of a line, passing through a given point that is parallel or perpendicular to a given line. Know that parallel lines have the same slope. Know that perpendicular lines have opposite reciprocal slopes. Determine whether a pair of lines are parallel, perpendicular or neither. Write the equation of the line passing through a given point that is parallel or perpendicular to a given line. New Jersey Center for Teaching and Learning: Geometry - Parallel and Perpendicular Lines Presentation Sec. 3.1 Identify Pairs of Lines and Angles Sec. 3.2 Use Parallel Lines and Transversals Sec. 3.3 Prove Lines are Parallel Sec. 3.4 Find and Use Slope of Lines Sec. 3.5 Write and Graph Equations of Lines Sec. 2.6 Prove Theorems about Perpendicular Lines Sec. 3.1 Parallel Lines and Transversals Sec. 3.2 Angles and Parallel Lines Sec. 3.3 Slopes of Lines Sec. 3.4 Equations of Lines Sec. 3.5 Proving Lines Parallel Sec. 3.6 Perpendiculars and Distance Khan Academy: Geometry - Angles and Intersecting Lines: Angles between Intersecting and Parallel Lines Virtual Nerd: Geometry - Parallel and Perpendicular Lines: Parallel Lines and Transversals

12 Geometry Points, Lines, Angles, and Planes G.PL.5: Explain and justify the process used to construct, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.), congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, and parallel and perpendicular lines. Explain and justify the process used to construct congruent segments and angles. Explain and justify the process used to construct angle bisectors and perpendicular bisectors. Explain and justify the process used to construct altitudes and medians. Explain and justify the process used to construct parallel and perpendicular lines. Sec. 1.4 Measure and Classify Angles Sec. 1.3 Distance and Midpoint Sec. 1.4 Angle Measure Sec. 1.5 Angle Relationships Sec. 3.5 Proving Lines Parallel New Jersey Center for Teaching and Learning: Geometry - Parallel and Perpendicular Lines Presentation