Quadrilateral Construction Exercise (Fixed Side)
2020-09-12 09:31
This GeoGebra example demonstrates how to construct quadrilaterals with one fixed side. Using Vector and Segment commands to build geometric objects, students can interactively drag vertices to form different quadrilaterals. The system leverages CountIf, Sequence, and IndexOf commands to automatically detect and count valid quadrilateral constructions, distinguishing results with blue and red segm
In collections
P4 Math: Constructing Quadrilaterals
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SetValue(ShowAns,false);

SetValue[Blue1a, (1,12)];
SetValue[Blue1b, (3,12)];
SetValue[Blue2a, (1,11)];
SetValue[Blue2b, (3,11)];
SetValue[Blue3a, (1,10)];
SetValue[Blue3b, (3,10)];
SetValue[Reda, (RandomElement({3, 4, 5, 6, 7, 8, 9, 11}), RandomElement({4, 5, 6, 7, 8, 9})) ];
SetValue[Redb0, (RandomElement({3, 4, 5, 6, 7, 8, 9, 11}), RandomElement({4, 5, 6, 7, 8, 9}))];

SetValue[Redb, If( Reda==Redb0, Redb0 + Vec03, Redb0 ) ];
SetValue[Redb, If( QuadType == 3 || QuadType == 4 , Reda + RanVecRectOrSq, If( QuadType == 5, Reda + RanVecRhom, Redb)) ];

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SetFixed(Blue1b,false);
SetFixed(Blue2a,false);
SetFixed(Blue2b,false);
SetFixed(Blue3a,false);
SetFixed(Blue3b,false);
SetFixed(Reda, true);
SetFixed(Redb, true);

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SetFixed(Blue2,false);
SetFixed(Blue3,false);
SetFixed(Red,true)"/>
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</element>
<command name="CountIf">
<input a0="A ≟ Reda" a1="A" a2="ListPoints"/>
<output a0="NumReda"/>
</command>
<element type="numeric" label="NumReda">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="CountIf">
<input a0="A ≟ Redb" a1="A" a2="ListPoints"/>
<output a0="NumRedb"/>
</command>
<element type="numeric" label="NumRedb">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="boolean" label="TestConnected1">
<value val="true"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="TestConnected2">
<value val="true"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="button" label="buttonShowAndCheckAns">
<show object="true" label="true"/>
<objColor r="255" g="255" b="102" alpha="1"/>
<bgColor r="127" g="0" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="43" y="369"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(ShowAns,true);

If( NumBlue1a == 2 && NumBlue1b == 2 && NumBlue2a == 2 && NumBlue2b == 2 && NumBlue3a == 2 && NumBlue3b == 2 && NumReda == 2 && NumRedb == 2, SetValue(TestConnected1, true), SetValue(TestConnected1, false))

If( ( Defined(Intersect(Blue1,Blue2)) && Defined(Intersect(Blue1,Blue3)) && Defined(Intersect(Blue2,Red)) && Defined(Intersect(Blue3,Red)) ) && (!Defined(Intersect(Blue1,Red))) && (!Defined(Intersect(Blue2,Blue3))) || ( Defined(Intersect(Blue1,Blue2)) && Defined(Intersect(Blue1,Red)) && Defined(Intersect(Blue2,Blue3)) && Defined(Intersect(Red,Blue3)) ) && (!Defined(Intersect(Blue1,Blue3))) && (!Defined(Intersect(Blue2,Red))) || ( Defined(Intersect(Blue1,Blue3)) && Defined(Intersect(Blue1,Red)) && Defined(Intersect(Blue3,Blue2)) && Defined(Intersect(Red,Blue2)) && (!Defined(Intersect(Blue1,Blue2))) && (!Defined(Intersect(Blue3,Red))) ) , SetValue(TestConnected2, true), SetValue(TestConnected2, false));

If( TestConnected1 && TestConnected2, SetValue(IsQuad, true), SetValue(IsQuad, false) );

If( ( (AreParallel(Blue1,Blue2) && !AreParallel(Blue3,Red) ) || (AreParallel(Blue1,Blue3) && !AreParallel(Blue2,Red) ) || (AreParallel(Blue1,Red) && !AreParallel(Blue2,Blue3) ) || (AreParallel(Blue2,Blue3) && !AreParallel(Blue1,Red) ) || (AreParallel(Blue2,Red) && !AreParallel(Blue1,Blue3) ) || (AreParallel(Blue3,Red) && !AreParallel(Blue1,Blue2)) ) && IsQuad, SetValue(IsTrape, true), SetValue(IsTrape, false) );

If( ( (AreParallel(Blue1,Blue2) && AreParallel(Blue3,Red) ) || (AreParallel(Blue1,Blue3) && AreParallel(Blue2,Red) ) || (AreParallel(Blue1,Red) && AreParallel(Blue2,Blue3) ) || (AreParallel(Blue2,Blue3) && AreParallel(Blue1,Red) ) || (AreParallel(Blue2,Red) && AreParallel(Blue1,Blue3) ) || (AreParallel(Blue3,Red) && AreParallel(Blue1,Blue2)) ) && IsQuad, SetValue(IsPara, true), SetValue(IsPara, false) );

If( (ArePerpendicular(Blue1,Blue2) || ArePerpendicular(Blue1,Blue3) ) && IsPara, SetValue(IsRect, true), SetValue(IsRect, false) );

If( Length(Blue1)==Length(Blue2) && Length(Blue1)==Length(Blue3) && IsPara, SetValue(IsRhom, true), SetValue(IsRhom, false) );

If( IsRect && IsRhom, SetValue(IsSq, true), SetValue(IsSq, false) );

If( QuadType==1 && IsQuad, SetValue[Answer, true], QuadType==2 && IsPara, SetValue[Answer, true], QuadType==3 && IsRect, SetValue[Answer, true], QuadType==4 && IsSq, SetValue[Answer, true], QuadType==5 && IsRhom, SetValue[Answer, true], QuadType==6 && IsTrape, SetValue[Answer, true], SetValue[Answer, false])
"/>
<font serif="false" sizeM="2" size="16" style="0"/>
<startPoint x="-14.8" y="0" z="1"/>
<caption val="檢查答案"/>
</element>
<element type="boolean" label="IsQuad">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="Answer">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="IsPara">
<value val="true"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="IsTrape">
<value val="false"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="IsSq">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="IsRect">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="boolean" label="IsRhom">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="ListQuadType" exp="{"四邊形", "平行四邊形", "長方形", "正方形", "菱形", "梯形"}"/>
<element type="list" label="ListQuadType">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="14" y="140"/>
<labelMode val="0"/>
<fixed val="true"/>
<ggbscript onUpdate="UpdateConstruction[];
SetValue(ShowAns,false);

SetValue[Blue1a, (1,12)];
SetValue[Blue1b, (3,12)];
SetValue[Blue2a, (1,11)];
SetValue[Blue2b, (3,11)];
SetValue[Blue3a, (1,10)];
SetValue[Blue3b, (3,10)];
SetValue[Reda, (RandomElement({3, 4, 5, 6, 7, 8, 9, 11}), RandomElement({4, 5, 6, 7, 8, 9})) ];
SetValue[Redb0, (RandomElement({3, 4, 5, 6, 7, 8, 9, 11}), RandomElement({4, 5, 6, 7, 8, 9}))];

SetValue[Redb, If( Reda==Redb0, Redb0 + Vec03, Redb0 ) ];
SetValue[Redb, If( QuadType == 3 || QuadType == 4 , Reda + RanVecRectOrSq, If( QuadType == 5, Reda + RanVecRhom, Redb)) ];

SetFixed(Blue1a,false);
SetFixed(Blue1b,false);
SetFixed(Blue2a,false);
SetFixed(Blue2b,false);
SetFixed(Blue3a,false);
SetFixed(Blue3b,false);
SetFixed(Reda, true);
SetFixed(Redb, true);

SetFixed(Blue1,false);
SetFixed(Blue2,false);
SetFixed(Blue3,false);
SetFixed(Red,true)"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<comboBox val="true"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<angleStyle val="0"/>
<symbolic val="true" />
</element>
<expression label="textInstruction" exp=""移動線段，製作
各類四邊形。""/>
<element type="text" label="textInstruction">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="153" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="-15.301437577417365" y="3.5913983205710323" z="1"/>
</element>
<element type="button" label="buttonGridDot">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="13" y="92"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(ShowDots, !ShowDots);
ShowGrid(2, !ShowDots)"/>
<font serif="false" sizeM="2" size="16" style="0"/>
<startPoint x="-15.308730327131256" y="2.803781351471117" z="1"/>
<caption val="格線 / 釘點"/>
</element>
<element type="button" label="buttonHideAns">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelOffset x="57" y="497"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="ShowAns=false"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="-14.6" y="-2.1" z="1"/>
<caption val="隱藏答案"/>
</element>
<expression label="textRight" exp=""正確""/>
<element type="text" label="textRight">
<show object="true" label="true" ev="40"/>
<condition showObject="ShowAns ∧ Answer"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="0" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2" size="16" style="0"/>
<startPoint x="-15" y="-1.4" z="1"/>
</element>
<expression label="textWrong" exp=""不對""/>
<element type="text" label="textWrong">
<show object="true" label="true" ev="40"/>
<condition showObject="ShowAns ∧ (¬Answer)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="215" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2" size="16" style="0"/>
<startPoint x="-13.5" y="-1.4" z="1"/>
</element>
<command name="IndexOf">
<input a0="SelectedElement[ListQuadType]" a1="ListQuadType"/>
<output a0="QuadType"/>
</command>
<element type="numeric" label="QuadType">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Sequence">
<input a0="Sequence[(s, t), s, 0, 23]" a1="t" a2="-3" a3="15"/>
<output a0="ListDots" randomResult="{{(0, -3), (1, -3), (2, -3), (3, -3), (4, -3), (5, -3), (6, -3), (7, -3), (8, -3), (9, -3), (10, -3), (11, -3), (12, -3), (13, -3), (14, -3), (15, -3), (16, -3), (17, -3), (18, -3), (19, -3), (20, -3), (21, -3), (22, -3), (23, -3)}, {(0, -2), (1, -2), (2, -2), (3, -2), (4, -2), (5, -2), (6, -2), (7, -2), (8, -2), (9, -2), (10, -2), (11, -2), (12, -2), (13, -2), (14, -2), (15, -2), (16, -2), (17, -2), (18, -2), (19, -2), (20, -2), (21, -2), (22, -2), (23, -2)}, {(0, -1), (1, -1), (2, -1), (3, -1), (4, -1), (5, -1), (6, -1), (7, -1), (8, -1), (9, -1), (10, -1), (11, -1), (12, -1), (13, -1), (14, -1), (15, -1), (16, -1), (17, -1), (18, -1), (19, -1), (20, -1), (21, -1), (22, -1), (23, -1)}, {(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0), (10, 0), (11, 0), (12, 0), (13, 0), (14, 0), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0), (21, 0), (22, 0), (23, 0)}, {(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1), (9, 1), (10, 1), (11, 1), (12, 1), (13, 1), (14, 1), (15, 1), (16, 1), (17, 1), (18, 1), (19, 1), (20, 1), (21, 1), (22, 1), (23, 1)}, {(0, 2), (1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2), (7, 2), (8, 2), (9, 2), (10, 2), (11, 2), (12, 2), (13, 2), (14, 2), (15, 2), (16, 2), (17, 2), (18, 2), (19, 2), (20, 2), (21, 2), (22, 2), (23, 2)}, {(0, 3), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3), (9, 3), (10, 3), (11, 3), (12, 3), (13, 3), (14, 3), (15, 3), (16, 3), (17, 3), (18, 3), (19, 3), (20, 3), (21, 3), (22, 3), (23, 3)}, {(0, 4), (1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4), (7, 4), (8, 4), (9, 4), (10, 4), (11, 4), (12, 4), (13, 4), (14, 4), (15, 4), (16, 4), (17, 4), (18, 4), (19, 4), (20, 4), (21, 4), (22, 4), (23, 4)}, {(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (7, 5), (8, 5), (9, 5), (10, 5), (11, 5), (12, 5), (13, 5), (14, 5), (15, 5), (16, 5), (17, 5), (18, 5), (19, 5), (20, 5), (21, 5), (22, 5), (23, 5)}, {(0, 6), (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6), (7, 6), (8, 6), (9, 6), (10, 6), (11, 6), (12, 6), (13, 6), (14, 6), (15, 6), (16, 6), (17, 6), (18, 6), (19, 6), (20, 6), (21, 6), (22, 6), (23, 6)}, {(0, 7), (1, 7), (2, 7), (3, 7), (4, 7), (5, 7), (6, 7), (7, 7), (8, 7), (9, 7), (10, 7), (11, 7), (12, 7), (13, 7), (14, 7), (15, 7), (16, 7), (17, 7), (18, 7), (19, 7), (20, 7), (21, 7), (22, 7), (23, 7)}, {(0, 8), (1, 8), (2, 8), (3, 8), (4, 8), (5, 8), (6, 8), (7, 8), (8, 8), (9, 8), (10, 8), (11, 8), (12, 8), (13, 8), (14, 8), (15, 8), (16, 8), (17, 8), (18, 8), (19, 8), (20, 8), (21, 8), (22, 8), (23, 8)}, {(0, 9), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (8, 9), (9, 9), (10, 9), (11, 9), (12, 9), (13, 9), (14, 9), (15, 9), (16, 9), (17, 9), (18, 9), (19, 9), (20, 9), (21, 9), (22, 9), (23, 9)}, {(0, 10), (1, 10), (2, 10), (3, 10), (4, 10), (5, 10), (6, 10), (7, 10), (8, 10), (9, 10), (10, 10), (11, 10), (12, 10), (13, 10), (14, 10), (15, 10), (16, 10), (17, 10), (18, 10), (19, 10), (20, 10), (21, 10), (22, 10), (23, 10)}, {(0, 11), (1, 11), (2, 11), (3, 11), (4, 11), (5, 11), (6, 11), (7, 11), (8, 11), (9, 11), (10, 11), (11, 11), (12, 11), (13, 11), (14, 11), (15, 11), (16, 11), (17, 11), (18, 11), (19, 11), (20, 11), (21, 11), (22, 11), (23, 11)}, {(0, 12), (1, 12), (2, 12), (3, 12), (4, 12), (5, 12), (6, 12), (7, 12), (8, 12), (9, 12), (10, 12), (11, 12), (12, 12), (13, 12), (14, 12), (15, 12), (16, 12), (17, 12), (18, 12), (19, 12), (20, 12), (21, 12), (22, 12), (23, 12)}, {(0, 13), (1, 13), (2, 13), (3, 13), (4, 13), (5, 13), (6, 13), (7, 13), (8, 13), (9, 13), (10, 13), (11, 13), (12, 13), (13, 13), (14, 13), (15, 13), (16, 13), (17, 13), (18, 13), (19, 13), (20, 13), (21, 13), (22, 13), (23, 13)}, {(0, 14), (1, 14), (2, 14), (3, 14), (4, 14), (5, 14), (6, 14), (7, 14), (8, 14), (9, 14), (10, 14), (11, 14), (12, 14), (13, 14), (14, 14), (15, 14), (16, 14), (17, 14), (18, 14), (19, 14), (20, 14), (21, 14), (22, 14), (23, 14)}, {(0, 15), (1, 15), (2, 15), (3, 15), (4, 15), (5, 15), (6, 15), (7, 15), (8, 15), (9, 15), (10, 15), (11, 15), (12, 15), (13, 15), (14, 15), (15, 15), (16, 15), (17, 15), (18, 15), (19, 15), (20, 15), (21, 15), (22, 15), (23, 15)}}"/>
</command>
<element type="list" label="ListDots">
<show object="true" label="true" ev="7"/>
<condition showObject="ShowDots"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="boolean" label="ShowDots">
<value val="false"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="ListVec01" exp="{Vec01, (2 * Vec01), (3 * Vec01), (4 * Vec01), Vec02, (2 * Vec02), Vec03, (2 * Vec03), Vec04, (2 * Vec04), Vec05, (2 * Vec05), Vec06, Vec10, (2 * Vec10), Vec11, (2 * Vec11), Vec12, (2 * Vec12), Vec16, Vec17}" />
<element type="list" label="ListVec01">
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="RandomElement">
<input a0="ListVec01"/>
<output a0="RanVecRectOrSq"/>
</command>
<element type="vector" label="RanVecRectOrSq">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="-1" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
</element>
<expression label="Redb0" exp="(RandomElement[{4, 5, 6, 7, 8, 9, 11, 12, 13, 14}], RandomElement[{4, 5, 6, 7, 8, 9}])" type="point" />
<element type="point" label="Redb0">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="11" y="9" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="ListVec02" exp="{Vec04, (2 * Vec04), (3 * Vec04), Vec05, (2 * Vec05), Vec06, Vec07, Vec08, Vec09, Vec10, (2 * Vec10), (3 * Vec10), Vec11, (2 * Vec11), Vec12, (2 * Vec12), Vec13, Vec14, Vec15, Vec16, Vec17, Vec18, Vec19, Vec20, Vec21}" />
<element type="list" label="ListVec02">
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="RandomElement">
<input a0="ListVec02"/>
<output a0="RanVecRhom"/>
</command>
<element type="vector" label="RanVecRhom">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3" y="1" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
</element>
</construction>
</geogebra>