Compass and Straightedge Construction: Copying an Angle
2020-12-24 08:23
This GeoGebra applet demonstrates the classic compass and straightedge construction of copying a given angle. The construction involves drawing circles, finding intersections, creating segments, and drawing circular arcs. It illustrates the application of the Side-Side-Side (SSS) congruence theorem in Euclidean geometry. Ideal for middle school geometry teaching and learning basic geometric constr
In collections
Points, Lines, and Angles
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.620.0" app="classic" platform="w" id="B02BF39D-EE7B-4776-8978-C3F1CDE925E1" xsi:noNamespaceSchemaLocation="https://ggb123.cn/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="800" height="600" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.125" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 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 , 538 | 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="true" location="1,1,1" size="584" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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="true" location="3" size="320" tab="ALGEBRA" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="true" location="3" size="300" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="100" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="22" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" 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="272" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<view id="1" visible="true" inframe="false" stylebar="false" location="" size="598" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 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 | 100001 100001" 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="798" height="598"/>
<coordSystem xZero="222.52942830033132" yZero="182.50211698011168" scale="14.036468323487492" yscale="14.036468323483183"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="11" 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>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="3"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="尺规作已知角" author="" date="">
<element type="point" label="O">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-28" y="38"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="10"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-100" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<expression label="B" exp="O + (10, 0)" type="point" />
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-18" y="39"/>
<labelMode val="0"/>
<coords x="10" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Line">
<input a0="B" a1="O"/>
<output a0="i_1"/>
</command>
<element type="line" label="i_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-10" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="c" a1="i_1"/>
<output a0="I" a1="J"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="10" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-10" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Semicircle">
<input a0="J" a1="B"/>
<output a0="k_1"/>
</command>
<element type="conicpart" label="k_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-100" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="7" y="32"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5.35162526936878" y="-1.9858763286462926" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="C"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 2 ∨ t ≟ 3"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.9858763286462926" y="5.35162526936878" z="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="O'" exp="O + (25, 0)" type="point" />
<element type="point" label="O'">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 1"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-32" y="33"/>
<labelMode val="0"/>
<coords x="25" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O'" a1="j"/>
<output a0="q"/>
</command>
<element type="conic" label="q">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="592.4164021835759" A3="0" A4="-25" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="q"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-1" y="40"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="30.388961673736087" y="-1.8822034681265685" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="P'" exp="O' + (12, 0)" type="point" />
<element type="point" label="P'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="37" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Segment[O', P']"/>
<output a0="M_1"/>
</command>
<element type="point" label="M_1">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-15" y="30"/>
<labelMode val="3"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<coords x="25" y="0" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<caption val="B'"/>
</element>
<command name="Segment">
<input a0="O'" a1="M_1"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O + (12, 0)" a1="O"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-12" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="k_1"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-22" y="-6"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="8.217872643783046" y="5.697944296898859" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="12"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-144" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Rotate">
<input a0="M_1" a1="Angle[B, O, A]" a2="O'"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<coords x="25" y="0" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
</element>
<command name="AngularBisector">
<input a0="A" a1="O" a2="B"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.29850689742591824" y="0.9544074770186748" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Mirror">
<input a0="C" a1="i"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.266356219976719" y="4.681294143785834" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="F" a1="Angle[C, O, C']" a2="O'"/>
<output a0="F'"/>
</command>
<element type="point" label="F'">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="28.175384233204344" y="4.743472650700266" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="O'" a1="F" a2="F'"/>
<output a0="r"/>
</command>
<element type="conicpart" label="r">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="592.4164021835759" A3="0" A4="-25" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="r"/>
<output a0="M_3"/>
</command>
<element type="point" label="M_3">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 3"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-45" y="-5"/>
<labelMode val="0"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<coords x="30.3889616737361" y="-1.882203468126529" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="O'" a1="F" a2="M_3"/>
<output a0="s"/>
</command>
<element type="conicpart" label="s">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="592.4164021835759" A3="0" A4="-25" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="s" a1="h"/>
<output a0="D'" a1=""/>
</command>
<element type="point" label="D'">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="O" a1="C" a2="C'"/>
<output a0="k"/>
</command>
<element type="conicpart" label="k">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-32.583597816424145" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="k"/>
<output a0="M_2"/>
</command>
<element type="point" label="M_2">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 2"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-8" y="-5"/>
<labelMode val="0"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<coords x="5.35162526936878" y="-1.985876328646292" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="O" a1="C" a2="M_2"/>
<output a0="p"/>
</command>
<element type="conicpart" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 2"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-32.583597816424145" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="p" a1="f"/>
<output a0="D" a1=""/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 2"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="d" a1="Ray[O, A]"/>
<output a0="P" a1=""/>
</command>
<element type="point" label="P">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.861447172539656" y="6.837533156278631" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="P" a1="O"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.837533156278631" y="-9.861447172539656" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="p" a1="g"/>
<output a0="E" a1=""/>
</command>
<element type="point" label="E">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 2"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="16" y="20"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="E"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="D'" a1="m"/>
<output a0="c_1"/>
</command>
<element type="conic" label="c_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="812.6594280584029" A3="0" A4="-30.708204430153508" A5="0"/>
<eqnStyle style="specific"/>
</element>
<element type="numeric" label="t">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="5" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="24" y="308"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,1]
StartAnimation[M_1,true]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="1、作射线O'B'"/>
</element>
<command name="Circle">
<input a0="O" a1="C"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-32.583597816424145" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_1" a1="Ray[D', H]"/>
<output a0="G" a1=""/>
</command>
<element type="point" label="G">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-24" y="5"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="M_2"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 2 ∨ t ≟ 3"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.985876328646292" y="5.35162526936878" z="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="G" a1="(2 * Angle[A, D, E])" a2="D'"/>
<output a0="G'"/>
</command>
<element type="point" label="G'">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-25" y="4"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="D'" a1="G" a2="G'"/>
<output a0="d_1"/>
</command>
<element type="conicpart" label="d_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="812.659428058403" A3="0" A4="-30.708204430153508" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="d_1"/>
<output a0="M_4"/>
</command>
<element type="point" label="M_4">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-43" y="16"/>
<labelMode val="0"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="1"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="D'" a1="G" a2="M_4"/>
<output a0="e_1"/>
</command>
<element type="conicpart" label="e_1">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≥ 4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="812.659428058403" A3="0" A4="-30.708204430153508" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="e_1" a1="s"/>
<output a0="E'" a1="" a2="" a3=""/>
</command>
<element type="point" label="E'">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="-6"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D'" a1="M_4"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="P'" a1="Angle[B, O, A]" a2="O'"/>
<output a0="P''"/>
</command>
<element type="point" label="P''">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="34.861447172539656" y="6.8375331562786315" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O'" a1="P''"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-6.8375331562786315" y="9.861447172539656" z="170.93832890696578"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="M_5"/>
</command>
<element type="point" label="M_5">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≟ 5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<coords x="25" y="0" z="1"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<caption val="A'"/>
</element>
<command name="Segment">
<input a0="O'" a1="M_5"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O'" a1="M_3"/>
<output a0="g_1"/>
</command>
<element type="segment" label="g_1">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 3"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.882203468126529" y="5.388961673736102" z="-47.05508670316323"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O'" a1="F"/>
<output a0="h_1"/>
</command>
<element type="segment" label="h_1">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 3"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.8822034681265685" y="5.3889616737360875" z="-47.055086703164214"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="24" y="345"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,2]
StartAnimation[M_2,true]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="2、以O为圆心画弧"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="23" y="381"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,3]
StartAnimation[M_3,true]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="3、以O'为圆心，同样半径画弧"/>
</element>
<element type="button" label="button4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="23" y="418"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,4]
SetValue[M_4,G]
StartAnimation[M_4,true]
"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="4、以D'为圆心，DE为半径画弧"/>
</element>
<element type="button" label="button5">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="22" y="458"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,5]
StartAnimation[M_5,true]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="5、作射线O'E'"/>
</element>
<element type="button" label="button6">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="25" y="270"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,0]
SetValue[M_1,O']
SetValue[M_2,C]
SetValue[M_3,F]
SetValue[M_4,G]
SetValue[M_5,O']"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="复位"/>
</element>
<command name="Segment">
<input a0="D'" a1="G"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""
拖动点A改变\angle AOB的大小\\当\angle AOB=180\degree时，只执行第1步、第5步即可""/>
<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"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="0.7" size="-8" style="0"/>
<absoluteScreenLocation x="24" y="500"/>
</element>
</construction>
</geogebra>