CK12 - Geometry

9. Samereasonas step 7


10. 
    


11. is a parallelogram 10. Definitionof a parallelogram

Provinga Quadrilateralis a ParallelogramGivenBisectingDiagonals

In the last lesson,you learnedthat in a parallelogram,the diagonalsbisecteachother. This can also be
turnedaroundinto a conversestatement.If you havea quadrilateralin whichthe diagonalsbisecteach
other, then the figureis a parallelogram.See if you can followthe proofbelowwhichshowshow this is ex-
plained.

Example 3

Completethe two-columnproofbelow.

• Given: , and


• Prove: is a parallelogram

Statement Reason

1. Given


2. 
   


3. 
   
   
   
   2. Given
   
   
   
   


4. Verticalanglesare congruent


5. 
   


6. If two sidesand the angle
   betweenthemare congruent,the two trian-

4.

gles are congruent

5. Correspondingpartsof congruenttrian-


6. gles are congruent


7. 
   
   
   
   6. Verticalanglesare congruent
   
   
   
   


8. If two sidesand the angle
   betweenthemare congruent,then the two

7.

trianglesare congruent

8. Correspondingpartsof congruenttriangle


9. are congruent


10. If two pairsof oppositesidesof a quadri-
    lateralare congruent,the figureis a parallel-


11. is a parallelogram

ogram