# Parallelogram

Pronunciation: /ˌpær.əˈlɛl.əˌgræm/ Explain
 Click on the blue points and drag them to change the figure. No matter where you drag them, the figure is a parallelogram. Can a parallelogram also be a rectangle? How? Can a parallelogram also be a cube? How? Manipulative 1 - Parallelogram Created with GeoGebra.

A parallelogram is a four sided polygon whose opposite sides are parallel.[2][3]

### Properties of Parallelograms

 Click on the blue points to change the figure. Click on the check boxes to show and hide the properties. Manipulative 2 - Parallelogram Properties Created with GeoGebra.
Properties of a parallelogram:
• The opposite angles of a parallelogram are congruent.
• The opposite sides of a parallelogram are congruent and parallel.
• The diagonals bisect each other.
• Each diagonal bisects the parallelogram into two congruent triangles.
• The sums of the angles of a parallelogram is 360° or radians.
• A tessellation of a plane can be created using any parallelogram.
• The area of a parallelogram is A = bh where A is the area, b is the base and h is the height.

### References

1. McAdams, David E.. All Math Words Dictionary, parallelogram. 2nd Classroom edition 20150108-4799968. pg 134. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Hilbert, David. The Foundations of Geometry. pp 28,33-35. Translated by Townsend, E. J., Ph. D.. The Open Court Publishing Company. 1950. Last Accessed 12/3/2018. http://www.gutenberg.org/files/17384/17384-pdf.pdf. Buy the book
3. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pp 23, 32-33. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/3/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/23/mode/1up/search/parallelogram. Buy the book
4. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pp 44, 34-36, 72-73. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 12/3/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/44/mode/1up/search/parallelogram. Buy the book

McAdams, David E. Parallelogram. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/parallelogram.html.

### Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
3/26/2019: Corrected formula for area in manipulative 2. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)