2. Reasoningand Proof.....................................................................................................................
InductiveReasoning
LearningObjectives
- Recognizevisualpatternsand numberpatterns.
- Extendand generalizepatterns.
- Write a counterexampleto a patternrule.
Introduction
You learnedaboutsomeof the basicbuildingblocksof geometryin Chapter1. Someof theseare points,
lines,planes,rays,and angles.In this sectionwe will beginto studywayswe canreasonaboutthese
buildingblocks.
One methodof reasoningis calledinductivereasoning. This meansdrawingconclusionsbasedon examples.
VisualPatterns
Somepeoplesay that mathematicsis the studyof patterns.Let’s look at somevisualpatterns.Theseare
patternsmadeup of shapes.
Example 1
A dot patternis shownbelow.A. How manydots wouldtherebe in the bottomrow of a fourthpattern?. Thereis one moredot in the bottomrow of eachfigurethan in the previousfigure.Also,the numberof
dots in the bottomrow is the sameas the figurenumber.
B. Whatwouldthe total numberof dots be in the bottomrow if therewere6 patterns?. The rowswouldcontain and dots.
The total numberof dots is.Example 2