三角形三线合一性质演示
2020-01-30 07:00
本 GeoGebra 范例动态演示了等腰三角形或等边三角形中“三线合一”的几何性质。通过构造三角形的高线、中线和角平分线，用户可以直观地观察到在特定条件下（如等腰三角形的底边），这三条特殊的线段会重合为同一条直线。该课件利用几何作图命令精确构建交点与线段，帮助学习者深入理解三角形的重要几何定理及其内在对称性。
所属专题
鹿梅初中数学几何课件与模型合集
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="A0E774D7-03DD-496D-8253-59F84CD1B475" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1266" height="601" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.3001579778830964" 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="false" location="1,1,1" size="500" 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="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 | 1009 || 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="198" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1536" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="380" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" 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="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" 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="true" 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" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1536" height="548"/>
<coordSystem xZero="630.0902038577068" yZero="283.82195650666796" scale="26.956837398306806" yscale="26.956837398306746"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="239" b="213"/>
<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>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<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="三角形三线合一" author="" date="">
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-9.44" y="-4.95" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.86" y="-4.79" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="f"/>
</command>
<element type="line" label="f">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.16000000000000014" y="7.579999999999999" z="36.0106"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<element type="point" label="M">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-9.5" y="3.79" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="N">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="10.9631512195122" y="4.248716097560977" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="Segment">
<input a0="M" a1="N"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="80" y="-1"/>
<labelMode val="0"/>
<coords x="-0.458716097560977" y="20.4631512195122" z="-81.91314604878052"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1.5" type="1" playing="false"/>
<coords x="9.710113002415603" y="4.220627129499537" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="f"/>
<output a0="高线_1"/>
</command>
<element type="line" label="高线_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-7.579999999999999" y="-0.16000000000000014" z="74.2779568990302"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="f" a1="高线_1"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<coords x="568.7886092946488" y="-261.0758748961551" z="57.481999999999985"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="OrthogonalLine">
<input a0="F" a1="高线_1"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.197120000000005" y="-435.71355999999986" z="-2069.961309199999"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.16000000000000014" y="7.579999999999999" z="36.0106"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="A"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="9.170627129499536" y="-19.1501130024156" z="-8.222339259481614"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="B"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="26"/>
<labelMode val="2"/>
<coords x="9.010627129499536" y="-11.570113002415603" z="-38.6610748207016"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="F"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.2481281984594279" y="11.755073402015394" z="55.84528314651921"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Midpoint">
<input a0="j"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="-1"/>
<labelMode val="3"/>
<coords x="-5.6499999999999995" y="-4.87" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="中线"/>
</command>
<element type="segment" label="中线">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.090627129499537" y="-15.360113002415602" z="-23.441707040091607"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="AngularBisector">
<input a0="A" a1="C" a2="B"/>
<output a0="p"/>
</command>
<element type="line" label="p">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5262123856605692" y="-0.8503531767315344" z="-1.5205580406655983"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Segment">
<input a0="C" a1="F"/>
<output a0="高线"/>
</command>
<element type="segment" label="高线">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="8.76249893104011" y="0.1849603995997917" z="-85.86550368437935"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="AngularBisector">
<input a0="A" a1="C" a2="B"/>
<output a0="n"/>
</command>
<element type="line" label="n">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5262123856605692" y="-0.8503531767315344" z="-1.5205580406655983"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="n" a1="j"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-4" y="-2"/>
<labelMode val="3"/>
<coords x="-19.095898157763358" y="-18.705934448561994" z="3.852633375030068"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="$%n$"/>
</element>
<command name="Segment">
<input a0="C" a1="E"/>
<output a0="角平分线"/>
</command>
<element type="segment" label="角平分线">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-43" y="29"/>
<labelMode val="0"/>
<coords x="9.075990364890707" y="-14.66669627907227" z="-26.22623583634167"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="M" a1="N"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.458716097560977" y="20.4631512195122" z="-81.91314604878052"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="C" a1="F" a2="A"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.5707963267948965"/>
<show object="true" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-28" y="-22"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<expression label="text1" exp=""三角形“三线合一”性质的探究""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2" size="16" style="1"/>
<absoluteScreenLocation x="487" y="57"/>
</element>
<expression label="text2" exp=""拖动点Ｃ，观察图形的变化""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="-5.911168281737051" y="6.102947795835829" z="1"/>
</element>
</construction>
</geogebra>