四边形自由构造与分类判定
2020-09-12 09:27
本GeoGebra范例提供了一个互动环境，允许用户自由构造四边形。系统通过内置的几何与逻辑判定算法，自动识别所绘图形的类型，包括平行四边形、梯形、正方形、长方形和菱形等，并即时反馈构造结果。适合学生探索四边形的几何性质与分类标准。
所属专题
小学四年级数学：制作四边形
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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[Blue4a, (1,9)];
SetValue[Blue4b, (3,9)];

SetFixed(Blue1a,false);
SetFixed(Blue1b,false);
SetFixed(Blue2a,false);
SetFixed(Blue2b,false);
SetFixed(Blue3a,false);
SetFixed(Blue3b,false);
SetFixed(Blue4a,false);
SetFixed(Blue4b,false);

SetFixed(Blue1,false);
SetFixed(Blue2,false);
SetFixed(Blue3,false);
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<keepTypeOnTransform val="true"/>
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<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
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<command name="CountIf">
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<output a0="NumBlue1b"/>
</command>
<element type="numeric" label="NumBlue1b">
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<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
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<command name="CountIf">
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<output a0="NumBlue2a"/>
</command>
<element type="numeric" label="NumBlue2a">
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<command name="CountIf">
<input a0="A ≟ Blue2b" a1="A" a2="ListPoints"/>
<output a0="NumBlue2b"/>
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<element type="numeric" label="NumBlue2b">
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<command name="CountIf">
<input a0="A ≟ Blue3a" a1="A" a2="ListPoints"/>
<output a0="NumBlue3a"/>
</command>
<element type="numeric" label="NumBlue3a">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="CountIf">
<input a0="A ≟ Blue3b" a1="A" a2="ListPoints"/>
<output a0="NumBlue3b"/>
</command>
<element type="numeric" label="NumBlue3b">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="CountIf">
<input a0="A ≟ Blue4a" a1="A" a2="ListPoints"/>
<output a0="NumBlue4a"/>
</command>
<element type="numeric" label="NumBlue4a">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="CountIf">
<input a0="A ≟ Blue4b" a1="A" a2="ListPoints"/>
<output a0="NumBlue4b"/>
</command>
<element type="numeric" label="NumBlue4b">
<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="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="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 && NumBlue4a == 2 && NumBlue4b == 2, SetValue(TestConnected1, true), SetValue(TestConnected1, false))

If( ( Defined(Intersect(Blue1,Blue2)) && Defined(Intersect(Blue1,Blue3)) && Defined(Intersect(Blue2,Blue4)) && Defined(Intersect(Blue3,Blue4)) && (!Defined(Intersect(Blue1,Blue4))) && (!Defined(Intersect(Blue2,Blue3)))) || ( Defined(Intersect(Blue1,Blue2)) && Defined(Intersect(Blue1,Blue4)) && Defined(Intersect(Blue2,Blue3)) && Defined(Intersect(Blue4,Blue3)) && (!Defined(Intersect(Blue1,Blue3))) && (!Defined(Intersect(Blue2,Blue4))) ) || ( Defined(Intersect(Blue1,Blue3)) && Defined(Intersect(Blue1,Blue4)) && Defined(Intersect(Blue3,Blue2)) && Defined(Intersect(Blue4,Blue2)) && (!Defined(Intersect(Blue1,Blue2))) && (!Defined(Intersect(Blue3,Blue4))) ) , SetValue(TestConnected2, true), SetValue(TestConnected2, false));

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

If( ( (AreParallel(Blue1,Blue2) && !AreParallel(Blue3,Blue4) ) || (AreParallel(Blue1,Blue3) && !AreParallel(Blue2,Blue4) ) || (AreParallel(Blue1,Blue4) && !AreParallel(Blue2,Blue3) ) || (AreParallel(Blue2,Blue3) && !AreParallel(Blue1,Blue4) ) || (AreParallel(Blue2,Blue4) && !AreParallel(Blue1,Blue3) ) || (AreParallel(Blue3,Blue4) && !AreParallel(Blue1,Blue2)) ) && IsQuad, SetValue(IsTrape, true), SetValue(IsTrape, false) );

If( ( (AreParallel(Blue1,Blue2) && AreParallel(Blue3,Blue4) ) || (AreParallel(Blue1,Blue3) && AreParallel(Blue2,Blue4) ) || (AreParallel(Blue1,Blue4) && AreParallel(Blue2,Blue3) ) || (AreParallel(Blue2,Blue3) && AreParallel(Blue1,Blue4) ) || (AreParallel(Blue2,Blue4) && AreParallel(Blue1,Blue3) ) || (AreParallel(Blue3,Blue4) && 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"/>
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<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="Answer">
<value val="false"/>
<show object="false" label="true"/>
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<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
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<element type="boolean" label="IsPara">
<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="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="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="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"/>
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<layer val="0"/>
<labelOffset x="14" y="140"/>
<labelMode val="0"/>
<fixed val="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">
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<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="153" alpha="255"/>
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<fixed val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="-15.301437577417365" y="3.5913983205710323" z="1"/>
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<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"/>
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<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"/>
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<expression label="textRight" exp=""正確""/>
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<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"/>
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<labelMode val="0"/>
<font serif="false" sizeM="2" size="16" style="0"/>
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<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"/>
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<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>
</construction>
</geogebra>