Geometric Construction: Drawing Segments and Angles
2020-04-22 09:16
This GeoGebra applet demonstrates fundamental geometric construction techniques, focusing on how to construct segments and angles using points, circles, segments, and intersections. With step-by-step controls and text instructions, it guides users through the process of building plane geometry figures, making it ideal for beginners learning the principles of compass and straightedge constructions.
In collections
Compass and Straightedge Constructions
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.578.0" app="classic" platform="w" id="C40E14C1-E356-4159-8F9A-A364B1756EB3" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="858" height="466" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.4428904428904429" 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 | 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="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="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="true" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="858" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="380" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="true" location="1" size="150" 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="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="383" window="100,100,700,550" />
<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="43" visible="false" inframe="false" stylebar="false" location="1" size="450" 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="0"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="857" height="464"/>
<coordSystem xZero="88.62921546322768" yZero="98.260458294783" scale="31.900905013495994" yscale="31.900905013495994"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="0" rightAngleStyle="1" checkboxSize="26" gridType="3" lockedAxesRatio="1"/>
<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"/>
<labelStyle axes="0" serif="true"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" selectionAllowed="false"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="false" selectionAllowed="false"/>
</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="作1条线段等于已知线段" author="" date="">
<element type="numeric" label="step">
<value val="3"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612"/>
<bgColor r="0" g="0" b="0" alpha="102"/>
<layer val="1"/>
<labelOffset x="-51" y="-9"/>
<labelMode val="1"/>
<slider min="0" max="3" absoluteScreenLocation="true" width="200" x="487" y="388" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="bnext">
<show object="true" label="true"/>
<condition showObject="step < 3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="709" y="367"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="step=step+1
"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="下一步"/>
</element>
<element type="button" label="bprev">
<show object="true" label="true"/>
<condition showObject="step > 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="1"/>
<labelOffset x="380" y="368"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="step=step-1"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="上一步"/>
</element>
<element type="point" label="O">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="N" exp="(5, 0)" type="point"/>
<element type="point" label="N">
<show object="true" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="5" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="N"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="-6" y="-22"/>
<labelMode val="0"/>
<coords x="0" y="5" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(-1, -6)" a1="(7, -6)"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<condition showObject="step > 0"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="8" z="48"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<condition showObject="step > 0"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="1"/>
<labelOffset x="-12" y="45"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="-6" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="a"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<condition showObject="step > 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="30" 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="11" A3="0" A4="0" A5="6"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c" a1="f" a2="1"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<condition showObject="step > 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelOffset x="4" y="36"/>
<labelMode val="0"/>
<coords x="5" y="-6" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false" ev="4"/>
<condition showObject="step > 2"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="5" z="30"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""
① 作1条直线,在上取一点A""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<condition showObject="step > 0"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<absoluteScreenLocation x="375" y="90"/>
</element>
<expression label="text1_1" exp=""
② 以A为圆心、a为半径作圆,交直线于B""/>
<element type="text" label="text1_1">
<show object="true" label="false" ev="40"/>
<condition showObject="step > 1"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<absoluteScreenLocation x="375" y="151"/>
</element>
<expression label="text1_2" exp=""
③ 线段AB=a,即为所求。""/>
<element type="text" label="text1_2">
<show object="true" label="false" ev="40"/>
<condition showObject="step > 2"/>
<objColor r="153" g="51" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<absoluteScreenLocation x="375" y="208"/>
</element>
</construction>
</geogebra>