Angle between Lateral Faces of a Pyramid 1
2016-09-16 12:14
This GeoGebra applet demonstrates calculating and visualizing the dihedral angle between adjacent lateral faces of a pyramid. By constructing the apex, base polygon, and lateral edges using spheres, intersection lines, and midpoints, it accurately creates the plane angle. This model aids in intuitively understanding the angle between two planes in solid geometry, ideal for 3D geometry education.
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<input a0="A" a1="K" a2="C"/>
<output a0="β"/>
</command>
<element type="angle3d" label="β">
<angleStyle val="1"/>
<value val="1.6698593718618784"/>
<show object="true" label="true" ev="4"/>
<condition showObject="q"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-61" y="-26"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="Polygon">
<input a0="C" a1="A" a2="K"/>
<output a0="poly1" a1="k_1" a2="c_1" a3="a_1"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="q"/>
<objColor r="255" g="255" b="0" alpha="0.45"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="k_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="a_1">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="K"/>
<output a0="p"/>
</command>
<element type="segment3d" label="p">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="B" a1="K" a2="A"/>
<output a0="γ"/>
</command>
<element type="angle3d" label="γ">
<angleStyle val="1"/>
<value val="1.5707963267948963"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="Angle">
<input a0="B" a1="K" a2="C"/>
<output a0="δ"/>
</command>
<element type="angle3d" label="δ">
<angleStyle val="1"/>
<value val="1.570796326794897"/>
<show object="true" label="false" ev="4"/>
<condition showObject="o"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<element type="boolean" label="o">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="49" y="185"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Hint"/>
</element>
<element type="boolean" label="q">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="48" y="252"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Answer"/>
</element>
</construction>
</geogebra>