Pyramid with a Vertical Pole in Solid Geometry
2016-09-17 07:20
This GeoGebra example demonstrates a 3D solid geometry construction of a pyramid with a vertical pole. Using commands such as Sphere, Plane, Polygon, and OrthogonalLine, it constructs the spatial relationships between the pyramid's faces and the vertical pole, measuring various angles (α, β, γ, δ). It is suitable for learning concepts of line-plane angles, plane-plane angles, and spatial perpendic
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.279.0" id="4ac1f63f-8898-4d4d-949d-c3d41b2e5908" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1896" height="834" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.8201476793248945" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="1046,117,700,550" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3,3" size="300" window="100,100,600,400" />
<view id="1" visible="false" inframe="false" stylebar="false" location="1,3" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="455" window="100,100,250,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1" size="333" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="true" location="3" size="1555" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1896" height="834"/>
<coordSystem xZero="215.00000000000003" yZero="315" scale="50.00000000000001" yscale="50"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="333" height="834"/>
<coordSystem xZero="213" yZero="315.00000000000006" scale="49.99999999999999" yscale="50.00000000000002"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="2.722430494683163" yZero="2.424224360919929" zZero="-4.123659241121906" scale="39.727383922985965" xAngle="39" zAngle="-869.562526868982"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="2" showNumbers="false"/>
<plate show="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<expression label ="C" exp="(3.75, 0, 0)" type="point"/>
<element type="point3d" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="3.75" y="0" z="0" w="1"/>
<pointSize val="2"/>
</element>
<expression label ="a" exp="x = 0" type="plane"/>
<element type="plane3d" label="a">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="0" z="0" w="0"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Sphere">
<input a0="C" a1="6.25"/>
<output a0="b"/>
</command>
<element type="quadric" label="b">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="-25" A4="0" A5="0" A6="0" A7="-3.75" A8="0" A9="0"/>
</element>
<command name="Segment">
<input a0="(-12, 0, 0)" a1="(-6.4289, 0, 0)"/>
<output a0="f"/>
</command>
<element type="segment3d" label="f">
<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="Point">
<input a0="f"/>
<output a0="B"/>
</command>
<element type="point3d" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-8" y="41"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-12" y="0" z="0" w="1"/>
<pointSize val="4"/>
</element>
<command name="Sphere">
<input a0="B" a1="13"/>
<output a0="c"/>
</command>
<element type="quadric" label="c">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="-25" A4="0" A5="0" A6="0" A7="12" A8="0" A9="0"/>
</element>
<command name="IntersectConic">
<input a0="c" a1="b"/>
<output a0="d"/>
</command>
<element type="conic3d" label="d">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-25" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="Sphere">
<input a0="B" a1="12"/>
<output a0="e"/>
</command>
<element type="quadric" label="e">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="0" A4="0" A5="0" A6="0" A7="12" A8="0" A9="0"/>
</element>
<command name="Sphere">
<input a0="C" a1="3.75"/>
<output a0="i"/>
</command>
<element type="quadric" label="i">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="0" A4="0" A5="0" A6="0" A7="-3.75" A8="0" A9="0"/>
</element>
<element type="numeric" label="h">
<value val="-5"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="255" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="(-y(E))" max="3.53" absoluteScreenLocation="true" width="200" x="66" y="204" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<caption val="Topple Over"/>
</element>
<command name="Plane">
<input a0="y + (0 * z) = (-h)"/>
<output a0="g"/>
</command>
<element type="plane3d" label="g">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="1" z="0" w="-5"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Intersect">
<input a0="g" a1="d"/>
<output a0="A" a1="D_1"/>
</command>
<element type="point3d" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-16" y="-12"/>
<labelMode val="0"/>
<coords x="0" y="5" z="0" w="1"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="D_1">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="5" z="0" w="1"/>
<pointSize val="3"/>
</element>
<command name="Sphere">
<input a0="A" a1="5"/>
<output a0="j"/>
</command>
<element type="quadric" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="0" x1="0" y1="1" z1="0" x2="0" y2="0" z2="1"/>
<matrix A0="1" A1="1" A2="1" A3="0" A4="0" A5="0" A6="0" A7="0" A8="-5" A9="0"/>
</element>
<command name="IntersectConic">
<input a0="c" a1="j"/>
<output a0="k"/>
</command>
<element type="conic3d" label="k">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-24.075443786982248" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="IntersectConic">
<input a0="j" a1="i"/>
<output a0="p"/>
</command>
<element type="conic3d" label="p">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-9" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="IntersectConic">
<input a0="e" a1="j"/>
<output a0="q"/>
</command>
<element type="conic3d" label="q">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-21.301775147929007" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="IntersectConic">
<input a0="j" a1="i"/>
<output a0="r"/>
</command>
<element type="conic3d" label="r">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-9" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="q" a1="r"/>
<output a0="D_2" a1="D" a2="" a3=""/>
</command>
<element type="point3d" label="D_2">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.881784197001252e-16" y="0" z="0" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="7" y="2"/>
<labelMode val="0"/>
<coords x="8.881784197001252e-16" y="0" z="0" w="1"/>
<pointSize val="3"/>
</element>
<command name="Polygon">
<input a0="B" a1="D" a2="A"/>
<output a0="poly1" a1="a_1" a2="b_1" a3="d_1"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="191" g="255" b="0" alpha="0.49"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="a_1">
<show object="true" label="false" ev="4"/>
<objColor r="191" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="b_1">
<show object="true" label="false" ev="4"/>
<objColor r="191" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="d_1">
<show object="true" label="false" ev="4"/>
<objColor r="191" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="A" a1="C" a2="D"/>
<output a0="poly2" a1="d_2" a2="a_2" a3="c_1"/>
</command>
<element type="polygon3d" label="poly2">
<lineStyle thickness="1" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0.49"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="d_2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="a_2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="c_1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="B" a1="D" a2="A"/>
<output a0="α"/>
</command>
<element type="angle3d" label="α">
<angleStyle val="1"/>
<value val="1.5707963267948963"/>
<show object="true" label="false" ev="4"/>
<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="A" a1="D" a2="C"/>
<output a0="β"/>
</command>
<element type="angle3d" label="β">
<angleStyle val="1"/>
<value val="1.5707963267948968"/>
<show object="true" label="false" ev="4"/>
<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="A" a2="C"/>
<output a0="γ"/>
</command>
<element type="angle3d" label="γ">
<angleStyle val="1"/>
<value val="1.8195063158884195"/>
<show object="true" label="true" ev="4"/>
<condition showObject="o"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-77" y="22"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<command name="OrthogonalLine">
<input a0="D" a1="xOyPlane"/>
<output a0="l"/>
</command>
<element type="line3d" label="l">
<show object="true" label="false" ev="4"/>
<condition showObject="n"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coords ox="8.881784197001252e-16" oy="0" oz="0" ow="1" vx="0" vy="0" vz="1" vw="0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Intersect">
<input a0="l" a1="xOyPlane"/>
<output a0="P"/>
</command>
<element type="point3d" label="P">
<show object="true" label="true" ev="4"/>
<condition showObject="n"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.881784197001252e-16" y="0" z="0" w="1"/>
<pointSize val="3"/>
</element>
<command name="Segment">
<input a0="P" a1="A"/>
<output a0="m"/>
</command>
<element type="segment3d" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="n"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="15" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="P" a1="A" a2="D"/>
<output a0="δ"/>
</command>
<element type="angle3d" label="δ">
<angleStyle val="1"/>
<value val="0"/>
<show object="true" label="true" ev="4"/>
<condition showObject="n"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="18" y="24"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
<element type="boolean" label="n">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="50" y="325"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Show Projection of D"/>
</element>
<command name="Intersect">
<input a0="xOyPlane" a1="d"/>
<output a0="E" a1="F"/>
</command>
<element type="point3d" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="5" z="0" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="F">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-5" z="0" w="1"/>
<pointSize val="3"/>
</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="51" y="259"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Show∡BAC"/>
</element>
</construction>
</geogebra>