单位圆与菱形的向量旋转变换动态构造
2021-07-30 15:36
本 GeoGebra 范例演示基于单位圆的菱形（或一般四边形）几何构造。通过向量（Vector）、旋转（Rotate）、多边形（Polygon）及动态坐标（DynamicCoordinates）等命令，展示菱形的顶点如何由单位圆上的点经向量平移与旋转变换生成。构造中包含多个角度参数（α、β、γ、δ）与序列（Sequence）动画，可动态观察图形在不同参数下的形态变化，适用于探究菱形的对称性、边角关系及向量变换的几何意义。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.656.0" app="classic" platform="w" id="762933da-685b-4110-92d2-98d23790006b" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="950" height="514" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="200" window="0,0,400,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="950" window="0,0,400,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="266" tab="ALGEBRA" window="1205,367,470,828" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="16" visible="false" inframe="false" stylebar="false" location="0" size="227" window="915,562,500,500" />
<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="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="150" window="547,217,1066,951" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" 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="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 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="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="950" height="514"/>
<coordSystem xZero="479.497" yZero="429.7989999999996" scale="55" yscale="54.99999999999996"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="0" 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"/>
<grid distX="1" distY="1" distTheta="0.08726646259971647"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="C1">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.0455090909090905" y="4.469072727272723" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-29" y="30"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(C1,A+uCopy)
SetValue(C2,B+vCopy)"/>
<coords x="1" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="P"/>
</element>
<command name="Vector">
<input a0="A" a1="C1"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript onUpdate="SetValue(uCopy, u)"/>
<coords x="2.0455090909090905" y="4.469072727272723" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="A"/>
</element>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-23" y="23"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<selectionAllowed val="false"/>
<coords x="-8" y="0" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<caption val="A"/>
</element>
<expression label="E" exp="D + ((5 / sin(45°) * sin(65°)), 0)" type="point" />
<element type="point" label="E">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="21"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="-1.5914361794421144" y="0" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<caption val="B"/>
</element>
<command name="Rotate">
<input a0="E - (5, 0)" a1="-70°" a2="E"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-14" y="-9"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="-3.3015368960704583" y="4.698463103929542" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<caption val="C"/>
</element>
<expression label="G" exp="A + F - D" type="point" />
<element type="point" label="G">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.698463103929542" y="4.698463103929542" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="d" exp="0.05"/>
<element type="numeric" label="d">
<value val="0.05"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<expression label="H" exp="A + E - D" type="point" />
<element type="point" label="H">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.408563820557886" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Union">
<input a0="Sequence[(x(A) + (Length[u] * cos(t°)), y(A) + (Length[u] * sin(t°))), t, 0, 355, 5]" a1="{G}"/>
<output a0="VPoints"/>
</command>
<element type="list" label="VPoints">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="l1" exp="{Segment[A + (1, 0), H - (0.2, 0)], Ray[H, H + (1, 0)]}" />
<element type="list" label="l1">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Point">
<input a0="Ray[A + (1, 0), A + (2, 0)]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="6" y="32"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(C2,B+vCopy)
SetValue(C1,A+uCopy)
"/>
<coords x="5.427327272727272" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="Q"/>
</element>
<command name="DynamicCoordinates">
<input a0="C1" a1="x(ClosestPoint[VPoints, C1])" a2="y(ClosestPoint[VPoints, C1])"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="2" y="1"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.077146979791612" y="4.454456073078639" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="R"/>
</element>
<command name="Angle">
<input a0="B" a1="A" a2="C"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<angleStyle val="1"/>
<value val="1.1344640137963142"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="30" y="-11"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="45"/>
</element>
<element type="point" label="C2">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.5727818181818174" y="6.10543636363636" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="B" a1="C2"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript onUpdate="SetValue(vCopy, v)"/>
<coords x="-1.8545454545454545" y="6.10543636363636" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="B"/>
</element>
<command name="Sequence">
<input a0="(x(B) + (round(Length[v]) * cos(t°)), y(B) + (round(Length[v]) * sin(t°)))" a1="t" a2="0" a3="355" a4="5"/>
<output a0="UPoints" randomResult="{(11.427327272727272, 0), (11.404495461277746, 0.522934456485949), (11.336173790800519, 1.041889066001582), (11.222882230461682, 1.5529142706151244), (11.065482997442722, 2.0521208599540124), (10.86517399494717, 2.5357095704441965), (10.623479695433904, 2.9999999999999996), (10.342239538461222, 3.4414586181062763), (10.023593931441141, 3.8567256581192355), (9.669967959846558, 4.242640687119285), (9.284052930846508, 4.596266658713868), (8.868785890833548, 4.914912265733951), (8.427327272727272, 5.196152422706632), (7.963036843171468, 5.437846722219899), (7.479448132681284, 5.63815572471545), (6.980241543342396, 5.79555495773441), (6.469216338728854, 5.908846518073248), (5.950261729213221, 5.977168188550474), (5.427327272727272, 6), (4.904392816241322, 5.977168188550474), (4.38543820672569, 5.908846518073248), (3.8744130021121466, 5.79555495773441), (3.3752064127732595, 5.638155724715451), (2.891617702283076, 5.4378467222199), (2.427327272727273, 5.196152422706632), (1.9858686546209947, 4.91491226573395), (1.5706016146080355, 4.596266658713868), (1.1846865856079871, 4.242640687119286), (0.8310606140134045, 3.856725658119237), (0.5124150069933204, 3.4414586181062754), (0.23117485002063987, 2.9999999999999996), (-0.010519449492627508, 2.535709570444197), (-0.2108284519881778, 2.0521208599540133), (-0.3682276850071373, 1.5529142706151262), (-0.481519245345976, 1.0418890660015816), (-0.5498409158232018, 0.5229344564859492), (-0.5726727272727281, 0), (-0.5498409158232018, -0.5229344564859477), (-0.481519245345976, -1.0418890660015827), (-0.3682276850071382, -1.5529142706151249), (-0.21082845198817868, -2.052120859954012), (-0.010519449492628397, -2.5357095704441956), (0.23117485002063987, -3.000000000000001), (0.5124150069933213, -3.441458618106277), (0.8310606140134027, -3.8567256581192355), (1.1846865856079862, -4.242640687119285), (1.570601614608035, -4.596266658713867), (1.9858686546209938, -4.91491226573395), (2.4273272727272692, -5.196152422706631), (2.891617702283077, -5.4378467222199), (3.3752064127732604, -5.638155724715451), (3.8744130021121483, -5.79555495773441), (4.38543820672569, -5.908846518073248), (4.904392816241322, -5.977168188550474), (5.427327272727272, -6), (5.950261729213219, -5.977168188550474), (6.4692163387288515, -5.908846518073249), (6.980241543342394, -5.79555495773441), (7.479448132681286, -5.63815572471545), (7.963036843171469, -5.4378467222198985), (8.427327272727272, -5.196152422706632), (8.868785890833548, -4.914912265733951), (9.284052930846507, -4.596266658713869), (9.669967959846556, -4.242640687119286), (10.023593931441138, -3.8567256581192373), (10.342239538461222, -3.441458618106279), (10.623479695433902, -3.0000000000000027), (10.865173994947172, -2.535709570444195), (11.065482997442722, -2.0521208599540115), (11.222882230461682, -1.552914270615124), (11.336173790800519, -1.0418890660015823), (11.404495461277746, -0.5229344564859499)}"/>
</command>
<element type="list" label="UPoints">
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="DynamicCoordinates">
<input a0="C2" a1="x(ClosestPoint[UPoints, C2])" a2="y(ClosestPoint[UPoints, C2])"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="2" y="1"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.8744130021121466" y="5.79555495773441" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="R"/>
</element>
<command name="Angle">
<input a0="C'" a1="B" a2="A"/>
<output a0="δ"/>
</command>
<element type="angle" label="δ">
<angleStyle val="1"/>
<value val="1.308996938995747"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-55" y="-7"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="45"/>
</element>
<command name="Segment">
<input a0="C'" a1="B"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="22" y="-15"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="5.79555495773441" y="1.5529142706151253" z="-31.454373482701715"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F" a1="D"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-10" y="-1"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="4.698463103929542" y="-4.698463103929542" z="37.587704831436334"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="F"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-7" y="-4"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="-4.698463103929542" y="-1.710100716628344" z="-7.477304171367368"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="vector" label="uCopy">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="2.0455090909090905" y="4.469072727272723" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="A"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-29" y="-29"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="-4.454456073078639" y="2.077146979791612" z="4.454456073078639"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="12"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="0" y="4.427327272727272" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="vector" label="vCopy">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-1.8545454545454545" y="6.10543636363636" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="B"/>
</element>
<command name="Polygon">
<input a0="{A, B, C'}"/>
<output a0="t1"/>
</command>
<element type="polygon" label="t1">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<condition showObject="closed1 ≠ 0"/>
<objColor r="255" g="215" b="0" alpha="0.3100000023841858"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="Distance[C, C'] < d" a1="true" a2="false"/>
<output a0="closed1"/>
</command>
<element type="boolean" label="closed1">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text1" exp=""拖拉紅點，構作一個滿足以下條件的著色的△PQR：
∠P = ∠A, ∠Q = ∠B, QR = BC。
△PQR 是否必定全等於 △ABC？ ""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="15" y="37"/>
</element>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-10" y="10"/>
<labelMode val="2"/>
<selectionAllowed val="false"/>
<coords x="0" y="6.408563820557886" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="D" a1="E" a2="F"/>
<output a0="t3" a1="l" a2="m" a3="n"/>
</command>
<element type="polygon" label="t3">
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="215" b="0" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="l">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0" y="6.408563820557886" z="0"/>
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-4.698463103929542" y="-1.710100716628344" z="-7.477304171367368"/>
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="4.698463103929542" y="-4.698463103929542" z="37.587704831436334"/>
<lineStyle thickness="0" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="E" a1="D" a2="F"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="1"/>
<value val="0.7853981633974483"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="29" y="-10"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="45"/>
</element>
<command name="Angle">
<input a0="F" a1="E" a2="D"/>
<output a0="γ"/>
</command>
<element type="angle" label="γ">
<angleStyle val="1"/>
<value val="1.2217304763960306"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-54" y="-8"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="45"/>
</element>
<command name="If">
<input a0="B ≟ H" a1="true" a2="false"/>
<output a0="reached"/>
</command>
<element type="boolean" label="reached">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>