基础几何作图：垂直线与直角的构造
2018-11-14 06:04
本 GeoGebra 范例展示了基础几何中垂直线与直角的构造方法。通过运用圆、点、直线和垂线（OrthogonalLine）等命令，演示了如何寻找交点、绘制线段并测量角度。该模型直观地呈现了垂直关系的几何性质，非常适合小学及初中阶段的几何教学，帮助学生深入理解直线相交、垂直及特殊角度的概念。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.504.0" app="classic" platform="d" id="3a322051-e822-411e-9b75-b026d1728cb4" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1608" height="864" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.12437810945273632" 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 | 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="1,1,1" 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="false" 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="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="370" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1589" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="200" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" 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" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1589" height="703"/>
<coordSystem xZero="408.3057851239669" yZero="401.7340345604811" scale="37.56574004507885" yscale="37.56574004507891"/>
<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="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>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="4.0" y="2.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="n">
<value val="6.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="5" max="10" absoluteScreenLocation="true" width="200.0" x="765.0" y="515.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="Circle">
<input a0="A" a1="n"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-16.0" A3="0.0" A4="-4.0" A5="-2.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.3056557081381719" y="4.801788269427373" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="旋轉"/>
</element>
<command name="Line">
<input a0="B" a1="A"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.801788269427373" y="5.305655708138172" z="-21.818464493985836"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="A" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-5.305655708138172" y="2.801788269427373" z="15.619046293697942"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.686183361380884" y="3.2994032089669645" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="3"/>
</element>
<command name="Intersect">
<input a0="c" a1="g" a2="2"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.801788269427373" y="7.305655708138173" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.006252499171208" y="2.115604908046489" z="11.793800180591855"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="f" a1="g"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.5707963267948966"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-53" y="-60"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<command name="Intersect">
<input a0="c" a1="f" a2="2"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.305655708138172" y="-0.801788269427373" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.191723624726564" y="2.4268311762526853" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="3"/>
</element>
<command name="Segment">
<input a0="F" 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="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.2286194456800583" y="6.113932083411608" z="-25.142341949543447"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.2994032089669645" y="-0.6861833613808841" z="-3.8252461131060898"/>
<lineStyle thickness="5" type="20" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="F" a1="A"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.4268311762526853" y="0.8082763752734361" z="-3.3238774555576134"/>
<lineStyle thickness="5" type="20" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""移動黑色十字點，改變線段長度。""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <fixed val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="9.841260000000014" y="7.686100000000002" z="1.0"/>
</element>
<expression label="text2" exp=""移動紅點可旋轉。""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="9.841260000000014" y="6.4882000000000035" z="1.0"/>
</element>
</construction>
</geogebra>