CK12 - Geometry

Whatis the sum of the measuresof the angles?

is the sum of the anglemeasuresin any quadrilateral.

Describewhichanglescometogetherat a givenpointto “surround”it.

One of eachof the anglesof the quadrilateralfit togetherat each“surrounded”point.

Will all quadrilateralstessellate?Yes, for the reasonsabove.

Tessellatingwith a RegularPolygon

TechnologyNote-“Virtual”PatternBlocks-TM

At the NationalLibraryof VirtualManipulativesyou can experimentwith PatternBlocks

T M

and othershapes.Try to put congruentrhombi,trapezoids,and otherquadrilateralstogetherto

make tessellations. The National Library of Virtual Manipulatives can be found at:

http://nlvm.usu.edu/en/nav/siteinfo.html.

A goodtessellationsite is

http://nlvm.usu.edu/en/nav/frames_asid_163_g_4_t_3.html?open=activities&from=ap-

plets/controller/query/query.htm?qt=tessellations&lang=en.

A squarewill tessellate.This is obvious,if you’veever seena chessboardor a graphpapergrid. A square
is a regularpolygon.Will all regularpolygonstessellate?

Example 2

Can a regularpentagontessellate?

Here’s whathappensif we try to “surround”a pointwith congruentregularpentagons.

Regularpentagonscan’tsurrounda point.Threearen’tenough,and four are too many. Rememberthat

eachangleof a regularpentagonmeasures Anglesof do not combineto equalthe that
it takesto surrounda point.