CK12 - Geometry

So,. Sinceoppositeanglesare congruent, will also measure.

Diagonalsin a Parallelogram

Thereis one morerelationshipto examinewithinparallelograms.Whenyou drawthe two diagonalsinside
parallelograms,they bisecteachother. This can be very usefulinformationfor examininglargershapesthat
may includeparallelograms.The easiestway to demonstratethis propertyis throughcongruenttriangles,
similarlyto how we provedoppositeanglescongruentearlierin the lesson.

Example 4

Use a two-columnprooffor the theorembelow.

• Given: is a parallelogram


• Prove: and

Statement Reason

1. is a parallelogram 1. Given.
   2. Oppositesidesin a parallelogramare
   congruent.

2.

3. 
   
   
   
   3. Verticalanglesare congruent.
   
   
   
   


4. 
   
   
   
   4. Alternateinterioranglesare congruent.
   
   
   5. AAS congruencetheorem:If two angles
      and one side in a triangleare congruent,the
   
   
   
   

5.

trianglesare congruent.

6. Correspondingpartsof congruenttrian-
   gles are congruent.


7. and

LessonSummary

In this lesson,we exploredparallelograms.Specifically, we havelearned:

• How to describeand provethe distancerelationshipsbetweenoppositesidesin a parallelogram.


• How to describeand provethe relationshipbetweenoppositeanglesin a parallelogram.


• How to describeand provethe relationshipbetweenconsecutiveanglesin a parallelogram.


• How to describeand provethe relationshipbetweenthe two diagonalsin a parallelogram.