Download Pre-AP Geometry Unit 2 – Deductive Reasoning

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