CK12 - Geometry

gruent.

Statement Reason

1. Given


2. is the bisector of


3. Definitionof an anglebisector(a bisectordivides
   an angleinto two congruentangles)

2.

3. Given


4. 
   


5. ReflexiveProperty


6. 
   


7. AAS CongruenceTheorem(if two pairsof angles
   and the correspondingnon-includedsidesare congru-

5.

ent, then the trianglesare congruent)

Noticehow the markingsin the triangleshelp in the proof.Wheneveryou do proofs,use arcs in the angles
and tic marksto showcongruentanglesand sides.

FlowProofs

Thoughtwo-columnproofsare the mosttraditionalstyle(in geometrytextbooks,at least!),thereare many
differentwaysof solvingproblemsin geometry. We alreadywrotea paragraphproofin an earlierlesson
that simplydescribed,step by step,the rationalebehindan assertion(whenwe showedwhy AAS is logically
equivalentto ASA).The two-columnstyleis easyto readand organizesideasclearly. Somestudents,
however, preferflow proofs.Flowproofsshowthe relationshipsbetweenideasmoreexplicitlyby usinga
chartthat showshow one idea will lead to the next.Like two-columnproofs,it is helpfulto alwaysremember
the end goal so you can identifywhatit is you needto prove.Sometimesit is easierto workbackwards!

The next examplerepeatsthe sameproofas the one above,but displayedin a flow style,ratherthan two
columns.

Example 4

Createa flow prooffor the statementbelow.

Given: is the bisectorof and

Prove: