CK12 - Geometry

We use arcs insidethe angleto showcongruencein anglesjust as tic marksshowcongruencein sides.

Fromthe markingsin the angleswe can see and.

By definition,if two trianglesare congruent,then you knowthat all pairsof correspondingsidesare congruent
and all pairsof correspondinganglesare congruent.This is sometimescalledCPCTC: Correspondingparts
of congruenttrianglesare congruent.

Example 1

Are the two trianglesbelowcongruent?

The questionaskswhetherthe two trianglesin the diagramare congruent.To identifywhetheror not the
trianglesare congruent,eachpair of correspondingsidesand anglesmustbe congruent.

Beginby examiningthe sides. and both haveone tic mark,so they are congruent. and

both havetwo tic marks,so they are congruentas well. and havethreetic markseach,so each
pair of sidesis congruent.

Nextyou mustcheckeachangle. and both haveone arc, so they are congruent.

becausethey eachhavetwo arcs.Finally, becausethey havethreearcs.

We can checkthat eachanglein the first trianglematcheswith its correspondinganglein the secondtriangle

by examiningthe sides. correspondswith becausethey are formedby the sideswith two and
threetic marks.Sinceall pairsof correspondingsidesand anglesare congruentin thesetwo triangles,we
concludethat the two trianglesare congruent.

CreatingCongruenceStatements

We havealreadybeenusingthe congruencesign whentalkingaboutcongruentsidesand congruent
angles.

For example,if you wantedto say that was congruentto , you couldwrite the followingstatement.

In Chapter1 you learnedthat the line above with no arrowsmeansthat is a segment(and not

a line or a ray). If you wereto read this statementout loud,you couldsay “Segment is congruentto

segment .”

Whendealingwith congruencestatementsinvolvinganglesor triangles,you can use othersymbols.Whereas

the symbol means“segment ,” the symbol means“angle .” Similarly, the symbol

means“triangle .”

Whenyou are creatinga congruencestatementof two triangles,the orderof the lettersis very important.
Correspondingpartsmustbe writtenin order. That is, the angleat first letterof the first trianglecorre-
spondswith the angleat the first letterof the secondtriangle,the anglesat the secondlettercorrespond,