How To Prove A Quadrilateral Is A Parallelogram

Flag Football For Dummies is here!  Get your game on and order your copy today! Dummies AI Browse Book & Article Categories

Book & Article Categories

closeTechnologyAcademics & The ArtsHome, Auto, & HobbiesBody, Mind, & SpiritBusiness, Careers, & MoneyCollections

Collections

Explore all collectionscloseBYOB (Be Your Own Boss)Be a Rad DadCareer ShiftingContemplating the CosmosFor Those Seeking Peace of MindFor the Aspiring AficionadoFor the Budding Cannabis EnthusiastFor the College BoundFor the Exam-Season CrammerFor the Game Day PrepperCustom Solutions

• Book & Article Categories
• Collections
• Custom Solutions
• Dummies AI

• Main Menu

• Book & Article Categories

• Technology
• Academics & The Arts
• Home, Auto, & Hobbies
• Body, Mind, & Spirit
• Business, Careers, & Money
• Dummies AI

• Main Menu

• Book & Article Categories

• Technology
• Academics & The Arts
• Home, Auto, & Hobbies
• Body, Mind, & Spirit
• Business, Careers, & Money
• Dummies AI

• Main Menu

• Collections

  Explore all collections

• BYOB (Be Your Own Boss)
• Be a Rad Dad
• Career Shifting
• Contemplating the Cosmos
• For Those Seeking Peace of Mind
• For the Aspiring Aficionado
• For the Budding Cannabis Enthusiast
• For the College Bound
• For the Exam-Season Crammer
• For the Game Day Prepper
• Dummies AI

HomeAcademics & The Arts ArticlesMath ArticlesGeometry ArticlesHow to Prove a Quadrilateral Is a ParallelogramByMark Ryan Updated2021-07-12 20:50:01From the bookGeometry For DummiesShare

• 
• 
• 
• 
• 

Download E-BookGeometry For Dummies Explore Book Geometry Essentials For Dummies Explore BookBuy NowBuy on AmazonBuy on WileySubscribe on PerlegoDownload E-BookGeometry For DummiesExplore Book Geometry Essentials For DummiesExplore BookBuy NowBuy on AmazonBuy on WileySubscribe on Perlego There are five ways in which you can prove that a quadrilateral is a parallelogram. The first four are the converses of parallelogram properties (including the definition of a parallelogram). Make sure you remember the oddball fifth one — which isn’t the converse of a property — because it often comes in handy:

• If both pairs of opposite sides of a quadrilateral are parallel, then it’s a parallelogram (reverse of the definition).

• If both pairs of opposite sides of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).

  Tip: To get a feel for why this proof method works, take two toothpicks and two pens or pencils of the same length and put them all together tip-to-tip; create a closed figure, with the toothpicks opposite each other. The only shape you can make is a parallelogram.

• If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).

• If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

  Tip: Take, say, a pencil and a toothpick (or two pens or pencils of different lengths) and make them cross each other at their midpoints. No matter how you change the angle they make, their tips form a parallelogram.

• If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram (neither the reverse of the definition nor the converse of a property).

  Tip: Take two pens or pencils of the same length, holding one in each hand. If you keep them parallel, no matter how you move them around, you can see that their four ends form a parallelogram.

The preceding list contains the converses of four of the five parallelogram properties. If you’re wondering why the converse of the fifth property (consecutive angles are supplementary) isn’t on the list, you have a good mind for details. The explanation, essentially, is that the converse of this property, while true, is difficult to use, and you can always use one of the other methods instead.

About This Article

This article is from the book: 

Geometry For Dummies

About the book author:

Mark Ryan has more than three decades’ experience as a calculus teacher and tutor. He has a gift for mathematics and a gift for explaining it in plain English. He tutors students in all junior high and high school math courses as well as math test prep, and he’s the founder of The Math Center on Chicago’s North Shore. Ryan is the author of Calculus For Dummies, Calculus Essentials For Dummies, Geometry For Dummies, and several other math books.

This article can be found in the category: 

GeometryGet a Subscription