三角形边上平分面积
2016-01-08 12:51
本范例演示了如何在三角形的边上构造特定的点或线段，使其将三角形的面积平分。通过GeoGebra的几何作图功能，利用中点、线段、直线和交点等基础工具，动态展示面积平分的几何性质与严谨的尺规作图过程，帮助直观理解三角形面积分割的数学原理。
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<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="1.9180817273746462" y="1.2885718502258316" z="1"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="0.5 ≤ t ≤ 1" a1="Polygon[A, P, G]" a2=""""/>
<output a0="poly4"/>
</command>
<element type="polygon" label="poly4">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="0.5 ≤ t ≤ 1" a1="Polygon[P, B, C, G]" a2=""""/>
<output a0="poly5"/>
</command>
<element type="polygon" label="poly5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="PointIn">
<input a0="poly5"/>
<output a0="點poly5_1"/>
</command>
<element type="point" label="點poly5_1">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="PointIn">
<input a0="poly4"/>
<output a0="點poly4_1"/>
</command>
<element type="point" label="點poly4_1">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
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<expression label="文字poly5" exp="" " + (Name[P]) + (Name[B]) + (Name[C]) + (Name[G]) + " 面積 = " + poly5" />
<element type="text" label="文字poly5">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
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</element>
<command name="PointIn">
<input a0="poly5"/>
<output a0="點poly5"/>
</command>
<element type="point" label="點poly5">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="文字poly4" exp="" " + (Name[A]) + (Name[P]) + (Name[G]) + " 面積 = " + poly4" />
<element type="text" label="文字poly4">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="807" y="123"/>
</element>
<command name="PointIn">
<input a0="poly4"/>
<output a0="點poly4"/>
</command>
<element type="point" label="點poly4">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="1 ≤ t ≤ 1.5" a1="Polygon[A, B, P, D]" a2=""""/>
<output a0="poly6"/>
</command>
<element type="polygon" label="poly6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="1 ≤ t ≤ 1.5" a1="Polygon[D, P, C]" a2=""""/>
<output a0="poly7"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="文字poly7" exp="" " + (Name[D]) + (Name[P]) + (Name[C]) + " 面積 = " + poly7" />
<element type="text" label="文字poly7">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="803" y="183"/>
</element>
<command name="PointIn">
<input a0="poly7"/>
<output a0="點poly7"/>
</command>
<element type="point" label="點poly7">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="文字poly6" exp="" " + (Name[A]) + (Name[B]) + (Name[P]) + (Name[D]) + " 面積 = " + poly6" />
<element type="text" label="文字poly6">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="803" y="215"/>
</element>
<command name="PointIn">
<input a0="poly6"/>
<output a0="點poly6"/>
</command>
<element type="point" label="點poly6">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="1.5 ≤ t ≤ 2" a1="Polygon[A, J, P, C]" a2=""""/>
<output a0="poly8"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="1.5 ≤ t ≤ 2" a1="Polygon[J, B, P]" a2=""""/>
<output a0="poly9"/>
</command>
<element type="polygon" label="poly9">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="文字poly9" exp="" " + (Name[J]) + (Name[B]) + (Name[P]) + " 面積 = " + poly9" />
<element type="text" label="文字poly9">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="966" y="61"/>
</element>
<command name="PointIn">
<input a0="poly9"/>
<output a0="點poly9"/>
</command>
<element type="point" label="點poly9">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="文字poly8" exp="" " + (Name[A]) + (Name[J]) + (Name[P]) + (Name[C]) + " 面積 = " + poly8" />
<element type="text" label="文字poly8">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="967" y="91"/>
</element>
<command name="PointIn">
<input a0="poly8"/>
<output a0="點poly8"/>
</command>
<element type="point" label="點poly8">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="2 ≤ t ≤ 2.5" a1="Polygon[A, I, P]" a2=""""/>
<output a0="poly10"/>
</command>
<element type="polygon" label="poly10">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="2 ≤ t ≤ 2.5" a1="Polygon[I, B, C, P]" a2=""""/>
<output a0="poly11"/>
</command>
<element type="polygon" label="poly11">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="文字poly10" exp="" " + (Name[A]) + (Name[I]) + (Name[P]) + " 面積 = " + poly10" />
<element type="text" label="文字poly10">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="971" y="125"/>
</element>
<command name="PointIn">
<input a0="poly10"/>
<output a0="點poly10"/>
</command>
<element type="point" label="點poly10">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="文字poly11" exp="" " + (Name[I]) + (Name[B]) + (Name[C]) + (Name[P]) + " 面積 = " + poly11" />
<element type="text" label="文字poly11">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="968" y="157"/>
</element>
<command name="PointIn">
<input a0="poly11"/>
<output a0="點poly11"/>
</command>
<element type="point" label="點poly11">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="2.5 ≤ t ≤ 3" a1="Polygon[A, B, K, P]" a2=""""/>
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</command>
<element type="polygon" label="poly12">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="2.5 ≤ t ≤ 3" a1="Polygon[P, K, C]" a2=""""/>
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</command>
<element type="polygon" label="poly13">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="文字poly13" exp="" " + (Name[P]) + (Name[K]) + (Name[C]) + " 面積 = " + poly13" />
<element type="text" label="文字poly13">
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<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="969" y="187"/>
</element>
<command name="PointIn">
<input a0="poly13"/>
<output a0="點poly13"/>
</command>
<element type="point" label="點poly13">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
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<expression label="文字poly12" exp="" " + (Name[A]) + (Name[B]) + (Name[K]) + (Name[P]) + " 面積 = " + poly12" />
<element type="text" label="文字poly12">
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<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
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</element>
<command name="PointIn">
<input a0="poly12"/>
<output a0="點poly12"/>
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<element type="point" label="點poly12">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>