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Chapter 2--Reasoning in Geometry

Essential Question:  How can inductive and deductive reasoning allow us to make and prove conjectures and to solve problems?

Unit Rationale:  Justifying your thinking is a component of mathematical argument and a precursor for proof writing.

As a result of this unit, students will be able to:

1.       Use inductive reasoning to find the nth term.

2.       Generalize linear and geometric patterns to find the nth term.

3.       Write a conjecture using inductive reasoning.

4.       Apply angle relationships to solve for an unknown.


·         Inductive/Deductive reasoning

·         Conjecture

·         Converse/Inverse/Contrapositive

·         Linear Pair

·         Vertical Angle

·         Parallel Lines

·         Corresponding sides

·         Alternate Exterior/Interior Angles

·         Same Side

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

G.1.A Distinguish between inductive and deductive reasoning.

G.2.A Know, prove, and apply theorems about parallel and perpendicular lines

G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

G.1.B Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counterexample.

Supporting Standards:

*G.1.C Use deductive reasoning to prove that a valid geometric statement is true.

G.3.K Analyze cross-sections of cubes, prisms, pyramids, and spheres and identify the resulting shapes.

Reasoning, Problem Solving, and Communication Standards:

*G.7.A Analyze a problem situation and represent it mathematically.

*G.7.B Select and apply strategies to solve problems.

G.7.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.

G.7.E Read and interpret diagrams, graphs, and texts containing the symbols, language and conventions of mathematics.

G.7.H Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.