Pre-AP Geometry Unit 2 Deductive Reasoning

Pre-AP Geometry Unit 2 – Deductive Reasoning

Day Date Topic Homework 1 9/15 Conditional Statements Deductive Reasoning 1 (conditional, hypothesis, conclusion, truth value, converse) 2 9/16 Conditional Statements Deductive Reasoning 2 (biconditional, counterexample, inverse, contrapositive 3 9/17 Activities for day 1 and day 2 4 9/20 Properties Deductive Reasoning 3 (deductive reasoning, addition property of Properties Worksheet equality, subtraction property of equality, multiplication property of equality, division property of equality, substitution property, distributive property, reflexive property, symmetric property, transitive property) 5 9/21 Pairs of Angles Deductive Reasoning 4 and and (vertical angles, linear pair angles, Pairs of Angles Worksheet 6 9/22 adjacent angles, complementary angles, Deductive Reasoning 5 supplementary angles, perpendicular More Pairs of Angles Worksheet bisector) 7 9/23 CFA/Quiz 8 9/24 Distance & Midpoint Formulas Selected questions from (Pythagorean Theorem, distance formula, Glencoe 1-3 midpoint formula) 9 9/27 Slopes of Parallel and Perpendicular lines Selected questions from and and (slope, slope-intercept form of linear Glencoe 3-3 (and 3-4 for Pre- 10 9/28 equation) AP) 11 9/29 Unit Review 12 9/30 Assessment Unit 2 – Deductive Reasoning Detailed Overview Use with unit calendar and overview

Big Ideas/Enduring Understanding

 Relationships among lines and angles can be used in everyday problems in design and application.  Logical reasoning establishes the basis for developing, testing, and justifying conjectures to form conclusions.  Deductive reasoning starts with a generalization and reasons to a specific statement. If the generalization is true and the reasoning is valid, the specific statement will always be true.  Inductive and deductive reasoning is used in developing patterns both algebraically and geometrically.

Essential Questions  How do inductive and deductive reasoning differ?  What special relationships occur between pairs of angles when parallel lines are cut by a transversal?  How can algebra be used to show geometric relationships?

Academic Concepts  slope  perpendicular  converse  transversal  constructions bisector  reasoning  same side interior  midpoint formula  bi-conditional  parallel lines angles  distance formula  conditional statement perpendicular lines  congruent  complementary  converse  corresponding segments  supplementary  informal proof angles  adjacent angles  angle bisector  counterexample  vertical angles  congruent angles  spherical geometry  deductive  alternate interior reasoning angles

Performance Descriptor  Use logical reasoning to determine if statements are true or false and give a counterexample.  Write a statement in if-ten form and write its converse, inverse, and/or contra-positive.  Explore the relationships between pairs of angles and parallel or perpendicular lines.  Use coordinate points to determine measures of length, including midpoint and distance.