CK12 - Geometry

2. Definitionof a parallelogram


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4. _ 3. AlternateInteriorAnglesTheorem


5. Definitionof a parallelogram


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7. 
   
   
   
   5. 
      

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8. 
   
   
   
   6. ReflexiveProperty
   
   
   
   


9. ASA TriangleCongruencePostulate


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11. Correspondingpartsof congruenttrian-
    gles are congruent

8.

The missingstatementin step 3 shouldbe relatedto the informationin step 2. and are parallel,

and is a transversal.Lookat the followingfigure(withthe othersegmentsremoved)to see the angles
formedby thesesegments:

Thereforethe missingstep is.

Work backwardsto fill in step 4. Sincestep 5 is about , the sideswe needparallelare and

. So step 4 is.

The missingreasonon step 5 will be the sameas the missingreasonin step 3: alternateinteriorangles.

Finally, to fill in the trianglecongruencestatement,BE CAREFULto makesure you matchup corresponding

angles.The correctform is. (Studentscommonlyget this reversed,so don’tfeel
bad if you take a few timesto get it correct!)

As you can imagine, the same process could be repeated with diagonal to show that

. Oppositeanglesin a parallelogramare congruent.Or, evenbetter, we can use the

fact that and togetherwith the AngleAdditionPostulateto show

. We leavethe detailsof theseoperationsfor you to fill in.

ConsecutiveAnglesin a Parallelogram

So at this point,you understandthe relationshipsbetweenoppositesidesand oppositeanglesin parallelo-
grams.Thinkaboutthe relationshipbetweenconsecutiveanglesin a parallelogram.You havestudiedthis
scenariobefore,but you can applywhatyou havelearnedto parallelograms.Examinethe parallelogram
below.