So.Finally, find the lengthof. The coordinatesof are (-4,5)and the coordinatesof are (-1,-2).So.Thus,in parallelogram , and. The oppositesidesare congruent.This exampleshowsthat in this parallelogram,the oppositesidesare congruent.In the last sectionwe
provedthis fact is true for all parallelogramsusingcongruenttriangles.Herewe haveshownan example
of this propertyin the coordinateplane.
OppositeAnglesin a Parallelogram
Not only are oppositesidesin a parallelogramcongruent.Oppositeanglesare also congruent.You can
provethis by drawingin a diagonaland showingASA congruencebetweenthe two trianglescreated.Re-
memberthat whenyou havecongruenttriangles,all correspondingpartswill be congruent.
Example 2
Fill in the blanksin the two-columnproofbelow.- Given: is a parallelogram
- Prove:
Statement Reason- is a parallelogram 1. Given