Bisecting the Area of a Triangle from a Point on a Side
2016-01-08 12:51
This applet demonstrates how to construct a specific point or segment on the side of a triangle to bisect its area. Using GeoGebra's geometric construction tools, such as midpoints, segments, lines, and intersections, it dynamically illustrates the geometric properties and rigorous construction process of area bisection, providing an intuitive understanding of the mathematical principles behind tr
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<element type="point" label="點poly5_1">
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<element type="text" label="文字poly5">
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<expression label="文字poly4" exp="" " + (Name[A]) + (Name[P]) + (Name[G]) + " 面積 = " + poly4" />
<element type="text" label="文字poly4">
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<element type="point" label="點poly4">
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<command name="If">
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<expression label="文字poly7" exp="" " + (Name[D]) + (Name[P]) + (Name[C]) + " 面積 = " + poly7" />
<element type="text" label="文字poly7">
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<expression label="文字poly6" exp="" " + (Name[A]) + (Name[B]) + (Name[P]) + (Name[D]) + " 面積 = " + poly6" />
<element type="text" label="文字poly6">
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<command name="PointIn">
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<element type="point" label="點poly6">
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<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
<pointSize val="5"/>
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<command name="If">
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<element type="polygon" label="poly8">
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<show object="false" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
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<command name="If">
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<expression label="文字poly9" exp="" " + (Name[J]) + (Name[B]) + (Name[P]) + " 面積 = " + poly9" />
<element type="text" label="文字poly9">
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<auxiliary val="true"/>
<coords x="NaN" y="NaN" z="NaN"/>
<coordStyle style="cartesian3d"/>
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<expression label="文字poly8" exp="" " + (Name[A]) + (Name[J]) + (Name[P]) + (Name[C]) + " 面積 = " + poly8" />
<element type="text" label="文字poly8">
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<command name="If">
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<element type="polygon" label="poly11">
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<expression label="文字poly10" exp="" " + (Name[A]) + (Name[I]) + (Name[P]) + " 面積 = " + poly10" />
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</construction>
</geogebra>