So, givenonly the informationthat the diagonalsbisecteachother, you can provethat the shapeis a paral-
lelogram.
Provinga Quadrilateralis a ParallelogramGivenOne Pair of Congruentand Parallel
Sides
The last way you can provea shapeis a parallelograminvolvesonly one pair of sides.
The proofis very similarto the previousproofsyou havedonein this sectionso we will leaveit as an exercise
for you to fill in. To set up the proof(whichoftenIS the mostdifficult step),drawthe following:
- Given:QuadrilateralABCDwith and
- Prove: is a parallelogram
Example 4
Examinethe quadrilateralon the coordinategrid below. Can you showthat it is a parallelogram?To showthat this shapeis a parallelogram,you couldfind all of the lengthsand compareoppositesides.
However, you can also studyone pair of sides.If they are both congruentand parallel,then the shapeis a
parallelogram.
Beginby showingtwo sidesare congruent.You can use the distanceformulato do this.Find the lengthof. Use for and for.