2-1 Patterns and Inductive Reasoning
Objective
To use inductive reasoning to make conjectures
Lesson Vocabulary
- inductive reasoning
- conjecture
- counterexample
“In the Solve It, you may have used inductive reasoning. Inductive reasoning is reasoning based on patterns you observe.”
Essential Understanding You can observe patterns in some number sequences and some sequences of geometric figures to discover relationships.
Problem 1 Finding and Using a Pattern
Look for a pattern. What are the next two terms in each sequence?
Plan
How do you look for a pattern in a sequence?
Look for a relationship between terms. Test that the relationship is consistent throughout the sequence.
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3, 9, 27, 81,…
Each term is three times the previous term. The next two terms are
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Each circle contains a polygon that has one more side than the preceding polygon. The next two circles contain a six-sided and a seven-sided polygon.
✓ Got It?
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What are the next two terms in each sequence?
- 45, 40, 35, 30,…
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Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs