CK12 - Geometry

Given: ;

Prove:

Statement Reason

1. ; Given
   Definitionof congruentsegments


2. 
   


3. Transitivepropertyof equality


4. Definitionof congruentsegments

AngleCongruenceProperties

Watch for proofsof the AngleCongruencePropertiesin the LessonExercises.

Reflexive:

Symmetric: If , then

Transitive: If and , then

LessonSummary

In this lessonwe lookedat old informationin a new light.We saw that the propertiesof equality—reflexive,
symmetric,transitive—converteasilyinto theoremsaboutcongruentsegmentsand angles.In the next
sectionwe’ll moveaheadinto new ground.Therewe’ll get to use all the toolsin our geometrytoolboxto
solveproblemsand to createnew theorems.

Pointsto Consider

We are aboutto transitionfrom introductoryconceptsthat are necessarybut not too “geometric”to the real
heartof geometry. We neededa certainamountof foundationmaterialbeforewe couldbeginto get into
moreunfamiliar, challengingconceptsand relationships.We havethe definitionsand postulates,and analogs
of the equalityproperties,as the foundation.Fromhere on out, we will be able to experiencegeometryon
a richerand deeperlevel.

LessonExercises

Provethe SegmentCongruenceProperties,in questions1-3.

1. Reflexive:


2. Symmetric:If , then

3.Transitive:If and , then

4. Is the followingstatementtrue?If it’s not, give a counterexample.If it is, proveit.

If and , then + = +

5. Give a reasonfor eachstatementin the proofbelow.