Polygon Geometric Construction and Interactive Demonstration
2022-03-28 09:16
This GeoGebra example demonstrates a geometric construction process based on points, segments, and polygons. Using commands such as Point, PointIn, Segment, and Polygon, it constructs multiple key points (A through J and their transformed counterparts G', G'', H', H'', etc.) and generates polygon poly1 along with associated segments. The example includes interactive elements like buttons and text,
In collections
Clever Perimeter Calculations
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</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="Q6" author="" date="">
<element type="point" label="A">
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<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Ray[A + (1, 0), A + (2, 0)]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
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<coords x="8" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Ray[A + (0, 1), A + (0, 2)]"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
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<coords x="0" y="5.950998827755715" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="PointIn">
<input a0="Polygon[B + F - A, F + (1, 0), A + (1, 1), B + (0, 1)]"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<condition showObject="(¬hint) ∧ a ∧ started"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="2" y="3.0000000000000027" z="1"/>
<pointSize val="6"/>
<pointStyle val="1"/>
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<expression label="E" exp="(x(D), y(F))" type="point" />
<element type="point" label="E">
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<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="5.950998827755715" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
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<expression label="C" exp="(x(B), y(D))" type="point" />
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8" y="3.0000000000000027" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(G, (x(D), If[y(G)<y(D), y(D), If[y(G)>y(E), y(E), y(G)]]))
SetValue(H, (x(C), If[y(H)<y(D), y(D), If[y(H)>y(E), y(E), y(H)]]))"/>
<coords x="2" y="3.000000000000002" z="1"/>
<pointSize val="5"/>
<pointStyle val="2"/>
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<element type="point" label="H">
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<objColor r="0" g="0" b="255" alpha="0"/>
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<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(G, (x(D), y(G)))
SetValue(H, (x(C), y(H)))"/>
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<pointSize val="5"/>
<pointStyle val="2"/>
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<command name="Segment">
<input a0="G" a1="H"/>
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<condition showObject="hint"/>
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<pointStyle val="0"/>
</element>
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<element type="point" label="G''">
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<layer val="2"/>
<labelMode val="0"/>
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<element type="point" label="I">
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<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(I, (If[x(I)<x(D), x(D), If[x(I)>x(C), x(C), x(I)]], y(E)))
SetValue(J, (If[x(J)<x(D), x(D), If[x(J)>x(C), x(C), x(I)]], y(D)))"/>
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<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(I, (If[x(I)<x(D), x(D), If[x(I)>x(C), x(C), x(I)]], y(E)))
SetValue(J, (If[x(J)<x(D), x(D), If[x(J)>x(C), x(C), x(I)]], y(D)))"/>
<coords x="2" y="3.000000000000002" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="I" a1="J"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="hint"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
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<lineStyle thickness="9" type="0" typeHidden="1"/>
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<keepTypeOnTransform val="true"/>
</element>
<expression label="I'" exp="I" type="point" />
<element type="point" label="I'">
<show object="true" label="false" ev="4"/>
<condition showObject="hint"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="2" y="5.950998827755715" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
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<expression label="I''" exp="I'" type="point" />
<element type="point" label="I''">
<show object="true" label="false" ev="4"/>
<condition showObject="hint"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="2" y="5.950998827755715" z="1"/>
<pointSize val="5"/>
<pointStyle val="2"/>
</element>
<expression label="J'" exp="J" type="point" />
<element type="point" label="J'">
<show object="true" label="false" ev="4"/>
<condition showObject="hint"/>
<objColor r="255" g="255" b="255" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="2" y="3.000000000000002" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="J''" exp="J'" type="point" />
<element type="point" label="J''">
<show object="true" label="false" ev="4"/>
<condition showObject="hint"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="2" y="3.000000000000002" z="1"/>
<pointSize val="5"/>
<pointStyle val="2"/>
</element>
<element type="boolean" label="hint">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="328" y="3"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetLineStyle[d, If[hint, 2, 0]]
SetLineStyle[c, If[hint, 2, 0]]
SetValue[G, D]
SetValue[H, C]
SetValue[I, E]
SetValue[J, D]
SetValue[started, true]"/>
<caption val="提示"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="D" a4="E" a5="F"/>
<output a0="poly1" a1="a_1" a2="b" a3="c" a4="d" a5="e" a6="f_1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="3" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment" label="a_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-19" y="12"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="8" z="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="8 cm"/>
</element>
<element type="segment" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-3.0000000000000027" y="0" z="24.00000000000002"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="-6" z="18.000000000000014"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-2.950998827755712" y="0" z="5.901997655511424"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="-2" z="11.90199765551143"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f_1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-38" y="7"/>
<labelMode val="3"/>
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<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="6 cm"/>
</element>
<expression label="text2" exp=""\red{拖拉顏色線}到適當位置。你能找出圖形的周界嗎？""/>
<element type="text" label="text2">
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<startPoint x="1.7138530967236605" y="7.985576727979899" z="1"/>
</element>
<element type="point" label="Point (dependent)">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="10"/>
</element>
<element type="boolean" label="a">
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<objColor r="0" g="0" b="255" alpha="0"/>
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<checkbox fixed="true"/>
<caption val="改變形狀"/>
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<element type="button" label="button1">
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<objColor r="0" g="0" b="0" alpha="0"/>
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<layer val="3"/>
<labelOffset x="558" y="6"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetLineStyle[d, 0]
SetLineStyle[c, 0]
SetValue[D, (2, 3)]
SetValue[G, D]
SetValue[H, C]
SetValue[I, E]
SetValue[J, D]
SetValue[started, false]
SetValue[a, false]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="重設"/>
</element>
<element type="boolean" label="started">
<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>
<expression label="text1" exp=""" + (LaTeX[If[(¬hint) ∧ a ∧ started, "拖拉×點，\;改變圖形形狀。\\圖形的周界是多少？", "下圖的周界是多少？"]]) + "\\" + (LaTeX[If[hint, text2, ""]]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<isLaTeX val="true"/>
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</element>
<element type="image" label="pic1">
<file name="46faf4dbc385f168a0cf0a9a5e23af7e/QSIP.png"/>
<inBackground val="false"/>
<absoluteScreenLocation x="3" y="379"/> <show object="true" label="false"/>
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<layer val="3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
</construction>
</geogebra>