(:title Basic Geometric Constructs: Compass and Straightedge with GeoGebra :) >>-<< %c12 exa%*** To use this offline today, you need to get the pre-release of GeoGebra 3.1: [[http://www.geogebra.org/cms/index.php?option=com_content&task=blogcategory&id=74&Itemid=59|Click here]] ***%% >>-<< (:div00 class="c12":) (:showhide init=hide div=div001 lshow="+" lhide="-":) What is a %red%pencil%%, a %reg%compass%%. and a %dkr%straightedge%% in GeoGebra? (:div00end:) (:div001 id=div001 style="margin-left:20px":) >>&<< Here is a little mathcast (video) explaining the tools we will use ... >>&<< -> %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct1/construct1.html|Attach:construct1_movie.jpg]] (:showhide init=hide div=div1100 lshow="+" lhide="-":) Read about it %s9% %newwin%[[http://mathcasts.org/mtwiki/uploads/Construct/Construct_A_Tools.pdf|(printable pdf)]]%% (:div1100 id=div1100 style="margin-left:20px":) Attach:Construct_A_Tools1.jpg >>&<< Attach:Construct_A_Tools2.jpg >>&<< Attach:Construct_A_Tools3.jpg >>&<< (:div1100end :) >>&<< (:div001end :) >>&<< (:div class="c11" :) (:showhide init=hide div=div1 lshow="+" lhide="-":) %bluegrass%Try the tools online%% or download: [[http://mathcasts.org/mtwiki/uploads/Construct/BasicConstruct.ggb|BasicConstruct.ggb]]. (:divend:) (:div1 id=div1 :) >>&<< (:div style="margin-left:20px":) (:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://geogebra.org/webstart/3.2/geogebra.jar" width="700" height="400" filename="http://mathcasts.org/mtwiki/uploads/Construct/BasicConstruct.ggb" showResetIcon="true" showToolBar="true" showMenuBar="true":) >>&<< (:divend:) (:div1end :) >>&<< (:div20 class="c12":) (:showhide init=hide div=div201 lshow="+" lhide="-":) %pra%What do we do when it says:%% %exa c11%Given ...%%? (:div20end:) (:div201 id=div201 style="margin-left:20px":) >>&<< Here is a little mathcast (video) explaining how to get the "givens" ... >>&<< -> %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct2/construct2.html|Attach:construct2_movie.jpg]] (:showhide init=hide div=div2100 lshow="+" lhide="-":) Read about it %s9% %newwin%[[http://mathcasts.org/mtwiki/uploads/Construct/Construct_B_Given.pdf|(printable pdf)]]%% (:div2100 id=div2100 style="margin-left:20px":) >>&<< (:showhide init=hide div=div101 lshow="+" lhide="-":) %c11%1. Given a point A ...%% (:div101 id=div101 style="margin-left:20px" :) Attach:Construct_B_Given1.jpg (:div101end :) >>&<< (:showhide init=hide div=div102 lshow="+" lhide="-":) %c11%2. Given a line m and a point A on m ...%% (:div102 id=div102 style="margin-left:20px" :) Attach:Construct_B_Given2.jpg (:div102end :) >>&<< (:showhide init=hide div=div103 lshow="+" lhide="-":) %c11%3. Given a line m ...%% (:div103 id=div103 style="margin-left:20px" :) Attach:Construct_B_Given3.jpg (:div103end :) >>&<< (:showhide init=hide div=div104 lshow="+" lhide="-":) %c11%4. Given an angle α ...%% (:div104 id=div104 style="margin-left:20px" :) Attach:Construct_B_Given4.jpg (:div104end :) >>&<< (:showhide init=hide div=div105 lshow="+" lhide="-":) %c11%5. Given a circle c ...%% (:div105 id=div105 style="margin-left:20px" :) Attach:Construct_B_Given5.jpg (:div105end :) >>&<< Attach:Construct_B_Given6.jpg >>&<< (:div2100end :) (:div201end :) >>&<< (:div220 class="c12":) (:showhide init=hide div=div221 lshow="+" lhide="-":) %mor%How do we do and undo?%% %s9%(a few more techniques)%% (:div220end:) (:div221 id=div221 style="margin-left:20px":) >>&<< Here is a little mathcast (video) explaining a few more useful techniques ... >>&<< -> %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct3/construct3.html|Attach:construct3_movie.jpg]] (:showhide init=hide div=div2210 lshow="+" lhide="-":) Read about it %s9% %newwin%[[http://mathcasts.org/mtwiki/uploads/Construct/Construct_C_Extras.pdf|(printable pdf)]]%% (:div2210 id=div2210 style="margin-left:20px":) >>&<< (:showhide init=hide div=div2211 lshow="+" lhide="-":) %c11%1. Using the Intersection Point Tool Attach:GgbActivity/intersect.jpg %% (:div2211 id=div2211 style="margin-left:20px" :) Attach:Construct_C_Extras1.jpg (:div2211end :) >>&<< (:showhide init=hide div=div2212 lshow="+" lhide="-":) %c11%2. Using the Compass Tool Attach:GgbActivity/compass.jpg %% - the tool that does: >>&<< (:div style="margin-left:20px":) %ref c10%"I need a circle with center A and with a radius the distance between B and C."%% >>&<< %pra c10%"a.k.a. Take your compass and stick the needle in point B and widen it until it reaches point C. %pra c10% Now stick the needle in point A and draw a circle."%% >>&<< (:divend:) (:div2212 id=div2212 style="margin-left:20px" :) Attach:Construct_C_Extras2.jpg (:div2212end :) >>&<<(:showhide init=hide div=div2213 lshow="+" lhide="-":) %c11%3. Undo/Redo Attach:GgbActivity/undo.jpg / Attach:GgbActivity/redo.jpg %% >>&<< (:div2213 id=div2213 style="margin-left:20px" :) Attach:Construct_C_Extras3.jpg (:div2213end :) >>&<<(:showhide init=hide div=div2214 lshow="+" lhide="-":) %c11%4. Forget the order in which you constructed? Look at the Construction Protocol. %% >>&<< (:div2214 id=div2214 style="margin-left:20px" :) Attach:Construct_C_Extras4.jpg (:div2214end :) >>&<<(:showhide init=hide div=div2215 lshow="+" lhide="-":) %c11%5. Making nice and readable constructs (decorating your objects) %% >>&<< (:div2215 id=div2215 style="margin-left:20px" :) Attach:Construct_C_Extras5.jpg (:div2215end :) >>&<< (:div2210end :) (:div221end :) >>&<< [table border=2 cellpadding=5] [row] [] (:div30 class="c12":) (:showhide init=show div=div3 lshow="+" lhide="-":) %exa%Seven basic compass and straightedge constructions%% %c9 red%UPDATED: May 2009%% (:div30end:) (:div3 id=div3 style="margin-left:20px":) (:showhide init=hide div=div31 lshow="+" lhide="-":) 1. Copy a line segment. [[InterA/construct_segment_copy|%c11%Complete interactivity%%]] (:div31 id=div31 style="margin-left:20px":) >>&<<%pra b%Given:%% A %pra%line segment%% with start point %red%A%% and a %pra%line%% with point %ref%P%% on it. >>&<<%sol b%Goal:%%   Construct a %exa%(:showhide init=hide div=div100 lshow="congruent line segment" lhide="congruent line segment":)%% on this line with start point %ref%P%%. (:div100 id=div100 :)            %s9%([[glossaryT/Congruent]]: the lengths of the segments are equal)%%. (:div100end :) >>&<< (:div style="margin-left:20px":) >>&<<[[InterA/construct_segment_copy|Attach:construct_segment_copy.jpg]] (:divend:) >>&<< (:div31end :) >>&<< (:showhide init=hide div=div32 lshow="+" lhide="-":) 2. Copy a triangle (side-side-side). %s9 sol%in progress%% (:div32 id=div32 style="margin-left:20px":) >>&<<%pra b%Given:%% A triangle ΔABC and a line with a point %ref%P%% on it. >>&<<%sol b%Goal:%% Construct a [[GlossaryT/congruent]] triangle ΔPRS such that the line segment {$\overline{PR}$} lies on the given line. (:div style="margin-left:20px":) >>&<<%popwin width=670 height=550 %coming soon (:divend:) >>&<< (:div32end :) >>&<< (:showhide init=hide div=div33 lshow="+" lhide="-":) 3. Copy an angle. [[InterA/construct_angle_copy|%c11%Complete interactivity%%]] (:div33 id=div33 style="margin-left:20px":) >>&<<%pra b%Given:%% An angle α with vertex A.>>&<< >>&<<%sol b%Goal:%% Copy angle α onto a line with point P so that P is the vertex.>>&<< >>&<< (:div101 id=div101 :)            %s9%([[glossaryT/Congruent]]: the sizes of the angles are equal)%%. (:div101end :) >>&<< (:div style="margin-left:20px":) >>&<<[[InterA/construct_angle_copy|Attach:construct_ang_copy1.jpg]] (:divend:) >>&<< (:div33end :) >>&<< (:showhide init=hide div=div34 lshow="+" lhide="-":) 4. bisect a line segment (in progress) (:div34 id=div34 :) >>&<<%pra b%Given:%% A line segment %ref%{$\overline {AB}$}%%. >>&<<%sol b%Goal:%% Construct the point C %ref%{$\overline {AB}$}%% that is halfway between %ref%A%% and %ref%B%%. >>&<< (:div style="margin-left:20px":) >>&<< %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct_par/construct_seg_bis.html|Attach:construct_seg_bis.jpg]] (:divend:) >>&<< -> %s8%Reference: [[http://www.mathopenref.com/constbisectline.html]]%% (:div34end :) >>&<< (:showhide init=hide div=div35 lshow="+" lhide="-":) 5. Construct a perpendicular (normal). %popwin width=670 height=550 %[[http://mathcasts.org/gg/enliven/mg/construct/perp/perp.htm|Mathcast]] %s9 sol%updated:30 August 2008%% (:div35 id=div35 style="margin-left:20px":) >>&<<%pra b%Given:%% a line %dkr%{$m \,\,$}%%with a point %ref%{$A \,\,$}%%on %dkr%{$m \,\,$}%%. >>&<<%sol b%Goal:%% Construct a line %mor%n%% passing through %ref%{$A \,\,$}%%and perpendicular (normal) to %dkr%{$m \,\,$}%%. (:div style="margin-left:20px":) >>&<< %popwin width=670 height=550 %[[http://mathcasts.org/gg/enliven/mg/construct/perp/perp.htm|Attach:construct_perp.jpg]] (:divend:) >>&<< -> %s8%Reference: [[http://www.mathopenref.com/constperpendray.html]] (:div35end :) >>&<< (:showhide init=hide div=div36 lshow="+" lhide="-":) 6. Bisect an angle (:div36 id=div36 style="margin-left:20px":) >>&<<%pra b%Given:%% An angle.>>&<< >>&<<%sol b%Goal:%% Construct the ray that bisects this angle (divides it into two equal angles).>>&<< >>&<< (:div style="margin-left:20px":) >>&<< %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct_ang_bis/construct_ang_bis.html|Attach:construct_ang_bis.jpg]] (:divend:) >>&<< -> %s8%Reference: [[http://www.mathopenref.com/constbisectangle.html]] (:div36end :) >>&<< (:showhide init=hide div=div37 lshow="+" lhide="-":) 7. Construct a parallel -(uses idea of transversal) (:div37 id=div37 style="margin-left:20px":) >>&<<%pra b%Given:%% A line %dkr%{$m \,\,$}%%and a point %ref%{$C \,\,$}%% '''NOT''' on %dkr%{$m \,\,$}%%. >>&<<%sol b%Goal:%% Construct (find) a line %mor%p%% passing through %ref%{$C \,\,$}%%and parallel to %dkr%{$m \,\,$}%%. >>&<< (:div style="margin-left:20px":) >>&<< %popwin width=670 height=550 %[[http://mathcasts.org/gg/constructs/construct_par/construct_par.html|Attach:construct_par.jpg]] (:divend:) >>&<< -> %s8%Reference: [[http://www.mathopenref.com/constparallel.html]]%% (:div37end :) >>&<< (:div3end :) [tableend] >>&<< ------ >>&<< %rel%Related themes: * [[construct/CompassTriangles|Second Level Constructions]] (compass and triangles) >>&<< ---- >>&<< (:showhide3 init=hide div=box4 lshow='Add comment' lhide='Close':) >>id=box4<< (:commentbox:) >><< >>&<< [table width=100% border=0] [row] [][[ggbActivity/Construct| Attach:main/tri_purple_up_a.gif ]] [[ggbActivity/Construct| Up one level]] [r](:html:) (:htmlend:) [tableend] %white%geometric, construct, construction, straightedge, compass, ruler, geogebra, application, geometry, program%%