(:title Squares:) >>nav_bar<<%reg%Mathcasts          %exa%Examples          %pra%Practice%%          %mor%More          %up%[[glossary/S|S]] >><< [[<<]] [table border=1 cellpadding=5 width=98%] [row] [] >>-<< %def b%Definition:%% In geometry, a %red%square%% is a 2-dimensional figure with four equal sides and four right (90°) angles. >>&<< (:div222 style="margin-left:20px":) (:showhide init=show div=div2 lshow="+" lhide="-":) %exa c11%Interactivity 1:%% Square %sol s8%(:showhide init=hide div=div22 lshow="+" lhide="-":) Directions for interactivity%% (:div2 id=div2 style="margin-left:40px":) >>&<< (:div22 id=div22 style="margin-left:20px" class="sol s9":) Click and drag points %ref c11%A%% and %ref c11%B%% to resize, move and rotate. (:div22end:) >>&<< (:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://www.geogebra.org/webstart/geogebra.jar" width="400" height="300" filename="http://mathcasts.org/gg/student/xtra/square.ggb" showResetIcon="true" showToolBar="false" showMenuBar="false":) (:div22end:) (:div2end :) (:div222end:) [tableend] >>&<< [table border=1 bordercolor=#ee8800 cellpadding=5 width=98%] [row] [l]%reg b%Basic formulas for square with side %mor c12%{$a$}%%: %up c11%perimeter is: {$L=4a$}%%, and %dkr c11%area is: {$A=a^2$}%%. (:div333 style="margin-left:40px":) >>&<< (:showhide init=hide div=div3 lshow="+" lhide="-" style="margin-left:40px":) Examples with perimeter and area of square >>&<< (:div3 id=div3 :) [table border=1 cellpadding=5 class=zebra] [row] [!c]Side length: %red%{$a$}%% [!c]Perimeter: %up%{$L=4a$}%% [!c]Area: %dke%{$A=a^2$}%% [row] [c]%red%{$3 \,cm$}%% [c]%up%{$4 \cdot 3\,cm=12\,cm$}%% [c]%dkr%{$3 \,cm \cdot 3 \,cm=3^2 \,cm^2=9 \,cm^2$}%% [row] [c]%red%{$2,5 \,m$}%% [c]%up%{$4 \cdot 2,5 \,m=10 \,m$}%% [c]%dkr%{$2,5 \,m \cdot 2,5 \,m=(2,5)^2 \,m^2=6,25 \,m^2$}%% [tableend] (:div3end :) (:div333end:) [tableend] >>-<< [table border=1 bordercolor=#660000 cellpadding=5 width=98%] [row] [l](:showhide init=hide div=div1 lshow="+" lhide="-":) %exa c11%Interactivity 2:%% Construct a square. >>-<< (:div1 id=div1 :) (:div11 style="margin-left:0px":) [table border=1 cellpadding=5 width=100%] [row] [l width=50%]1. %sol%Check out the square in the '''left window'''%%. (:div style="margin-left:20px":) >>&<< -< 1.a Choose the Attach:ggb/move.jpg icon. >>&<< -< 1.b Click and drag the slider button to increase or decrease the square size as desired. >>&<< -< 1.c Click and drag the point B to slant the square as desired. (:divend:) >>&<< -> %pra c10%Notice that the square ALWAYS remains a square.%% >>&<< [l width=50%]2. You do it in the '''right window'''. (:div style="margin-left:20px":) >>&<< -< 2.a Construct a square in the right window with the same properties. >>&<< -< 2.b If you need help, click to open a new window with %newwin%[[http://www.mathcasts.org/gg/student/quad/square/square1.html|complete directions]]. >>&<< >>&<< (:divend:) >>&<< -> %pra c10%Check that the square ALWAYS remains a square.%% [tableend] [table width=100%] [row] [c] (:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://www.geogebra.org/webstart/geogebra.jar" width="400" height="400" filename="http://mathcasts.org/gg/student/xtra/squareA.ggb" customToolBar="0 | " showResetIcon="true" showToolBar="true" showMenuBar="false":) [c] (:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://www.geogebra.org/webstart/geogebra.jar" width="400" height="400" filename="http://mathcasts.org/gg/student/xtra/squareB.ggb" customToolBar="0 | 18 | 34 | 4 | 5 | 16 || 46 || 40 " showResetIcon="true" showToolBar="true" showMenuBar="false":) [tableend] (:div11end :) (:div1end :) [tableend] >>-<< [table border=1 bordercolor=#6600cc cellpadding=5 width=98%] [row] []%mor b%Equivalent Definitions: * A square is a [[rectangle]] with 4 equal sides. * A square is a [[rhombus]] with 4 right angles. * A square is a [[regular polygon]] with 4 sides. >>&<< (:div style="margin-left:40px":) (:showhide init=hide div=div4 lshow="+" lhide="-":) Theorems (:div4 id=div4 :) *The diagonals of a square are of equal length (follows because a square is a rectangle). *The diagonals of a square intersect at right 90° angle (follows because a square is a rhombus). (:div4end :) (:divend:) [tableend] >>&<< (:html:) (:htmlend:) ------ >>&<< %rel%Related themes: * [[GlossaryT/paralelogram|Paralelogram]], [[GlossaryT/rectangle|Rectangle]] * [[GlossaryT/rhombus|Rhombus]], Trapezoid, Quadrilateral *Polygons, Triangles, Kite (Deltoid) >>&<< ---- >>&<< [table width=100%] [row] [][[glossary/T| Attach:main/tri_purple_up_a.gif ]] [[glossary/T| Up one level]] [r](:html:) (:htmlend:) [tableend]