CK12 - Geometry

Now we can see that (A), (S), and (A), which shows that

by ASA.

ProvingTrianglesCongruent

In geometrywe use proofsto showsomethingis true.You haveseena few proofsalready—theyare a
specialform of argumentin whichyou haveto justifyeverystep of the argumentwith a reason.Valid reasons
are definitions,postulates,or resultsfrom otherproofs.

One way to organizeyour thoughtswhenwritinga proofis to use atwo-columnproof.This is probablythe
mostcommonkind of proofin geometry, and it has a specificformat.In the left columnyou writestatements
that lead to whatyou wantto prove.In the right handcolumn,you writea reasonfor eachstep you take.
Mostproofsbeginwith the “given”information,and the conclusionis the statementyou are tryingto prove.
Here’s an example:

Example 3

Createa two-columnprooffor the statementbelow.

Given: is the bisectorof , and

Prove:

Rememberthat eachstep in a proofmustbe clearlyexplained.You shouldformulatea strategybeforeyou
beginthe proof.Sinceyou are tryingto provethe two trianglescongruent,you shouldlook for congruence
betweenthe sidesand angles.You knowthat if you can proveSSS,ASA,or AAS,you can provecongruence.
Sincethe giveninformationprovidestwo pairsof congruentangles,you will mostlikelybe able to showthe
trianglesare congruentusingthe ASA postulateor the AAS theorem.Noticethat both trianglesshareone

side.We knowthat side is congruentto itself , and now you havepairsof two congruent
anglesand non-includedsides.You can use the AAS congruencetheoremto provethe trianglesare con-