- Supposethat , , and are threeof four vertices(corners)of a parallelogram.
Give two possiblelocationsfor the fourthvertex, , if you knowthat the -coordinateof is.
- Dependingon whereyou chooseto put point in 4, the nameof the parallelogramyou drawwill change.
Sketcha pictureto showwhy. - If you knowthe parallelogramis named , whatis the slopeof the side parallelto?
- Again,assumingthe parallelogramis named , whatis the lengthof?
- Prove:If oppositesidesof a quadrilateralare congruent,then the quadrilateralis a parallelogram.
Given: with and
Prove: and (i.e., is a parallelogram).
- Prove:If a quadrilateralhas one pair of congruentparallelsides,then it is a parallelogram.
- Notein 9 that the parallelsidesmustalso be the congruentsidesfor that theoremto work.Sketcha
counterexampleto showthat if a quadrilateralhas one pair of parallelsidesand one pair of congruentsides
(whichare not the parallelsides)then the resultingfigureit is not necessarilya parallelogram.Whatkind of
quadrilateralscan you makewith this arrangement?
Answers
- a. , b. , c. , d. (note:you
needto find almostall anglemeasuresin the diagramto answerthis question)[Diff: 1-2]. - a. [Diff: 1]
- a. , b.
- can be at either or
- If is at the parallelogramwouldbe named (in red in the followingillustration).If
is at then the parallelogramwill take the name.