3D Geometric Demonstration of the Theorem of Three Perpendiculars
2019-02-15 12:47
This GeoGebra applet visually demonstrates the Theorem of Three Perpendiculars using 3D solid geometry constructions. The model includes key geometric elements such as planes, oblique lines, perpendiculars, and projections. Utilizing polygons, segments, and angle measurement tools, it clearly illustrates the property that if a line in a plane is perpendicular to the projection of an oblique line p
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<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="2"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="A" a1="C" a2="D"/>
<output a0="aACD"/>
</command>
<element type="angle3d" label="aACD">
<angleStyle val="1"/>
<value val="1.5707963267948966"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="153" b="255" alpha="0.5"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="60"/>
<selectionAllowed val="false"/>
</element>
<expression label="text1" exp=""A""/>
<element type="text" label="text1">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="16" style="1"/>
<startPoint exp="A"/>
<labelOffset x="-9" y="-65"/>
</element>
<expression label="text2" exp=""B""/>
<element type="text" label="text2">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="16" style="1"/>
<startPoint exp="B"/>
<labelOffset x="12" y="-45"/>
</element>
<expression label="text3" exp=""C""/>
<element type="text" label="text3">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="16" style="1"/>
<startPoint exp="C"/>
<labelOffset x="-23" y="18"/>
</element>
<expression label="text4" exp=""D""/>
<element type="text" label="text4">
<show object="true" label="false" ev="20"/>
<condition showObject="show ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="16" style="1"/>
<startPoint exp="D"/>
<labelOffset x="-34" y="13"/>
</element>
<expression label="text5" exp=""E""/>
<element type="text" label="text5">
<show object="true" label="false" ev="20"/>
<condition showObject="show ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="16" style="1"/>
<startPoint exp="E"/>
<labelOffset x="-16" y="-60"/>
</element>
<expression label="click" exp=""✔ 立體結構""/>
<element type="text" label="click">
<show object="true" label="false" ev="37"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="127" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="3"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<absoluteScreenLocation x="21" y="46"/>
<ggbscript val="SetValue(show, !show)
SetBackgroundColor(click, If(show, "Orange", "Yellow"))
SetValue(click, If(show, "✔ 立體結構", "顯示更多 ..."))"/>
</element>
<element type="boolean" label="show">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>