平行四边形的几何构造与高线演示
2018-10-03 17:39
本 GeoGebra 范例展示了平行四边形的基础几何构造过程。通过点、直线、线段及垂线等命令,动态构建了平行四边形及其相关辅助线。图中详细标注了底边与对应的高,直观演示了平行四边形的几何性质与面积计算要素,适合用于平面几何教学与面积公式推导。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.31.0" id="766f3606-d061-410c-9975-db19ed5c307e" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1032" height="746" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1937984496124031" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="162,94,700,550" />
<view id="4" toolbar="0 59 || 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 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1013" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 | 1 501 67 , 5 19 , 72 | 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 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="1013" height="587"/>
<coordSystem xZero="232.51194590533424" yZero="303.388204357626" scale="43.38842975206611" yscale="43.388429752066145"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" 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="10"/>
<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"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="平行四邊形" author="Hin Chan" date="9 12 月 2013">
<worksheetText above="平行四邊形的高和底" below=""/>
<element type="point" label="A">
<show object="true" label="false"/>
<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="9.068962770562774" y="3.8348519480519494" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="1"/>
</element>
<element type="point" label="B">
<show object="true" label="false"/>
<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="12.456962770562775" y="-2.388005194805189" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="1"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="a"/>
</command>
<element type="line" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.222857142857139" y="3.3880000000000017" z="-69.42733815510203"/>
<lineStyle thickness="1" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<element type="point" label="C">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.2788675324675347" y="3.558280519480521" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="1"/>
</element>
<command name="Line">
<input a0="C" a1="a"/>
<output a0="b"/>
</command>
<element type="line" label="b">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.222857142857139" y="3.3880000000000017" z="-20.013664359183693"/>
<lineStyle thickness="1" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Line">
<input a0="A" a1="C"/>
<output a0="c"/>
</command>
<element type="line" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.27657142857142825" y="-7.790095238095239" z="27.3656459102041"/>
<lineStyle thickness="1" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Line">
<input a0="B" a1="c"/>
<output a0="d"/>
</command>
<element type="line" label="d">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.27657142857142825" y="-7.790095238095239" z="-22.04802788571424"/>
<lineStyle thickness="1" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="b" a1="d"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="230.60706989811317" y="-131.66652007176174" z="49.41367379591834"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.27657142857142825" y="-7.790095238095239" z="27.3656459102041"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<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"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.222857142857139" y="3.3880000000000017" z="-69.42733815510203"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="D"/>
<output a0="底_1"/>
</command>
<element type="segment" label="底_1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="25" y="25"/>
<labelMode val="0"/>
<coords x="0.27657142857142825" y="-7.7900952380952395" z="-22.04802788571424"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="底_2"/>
</command>
<element type="segment" label="底_2">
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-3" y="12"/>
<labelMode val="0"/>
<coords x="6.222857142857139" y="3.388000000000001" z="-20.01366435918369"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="false"/>
<objColor r="255" 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="3.6763317665422353" y="-0.8452252165750456" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="2"/>
</element>
<command name="OrthogonalLine">
<input a0="E" a1="a"/>
<output a0="e"/>
</command>
<element type="line" label="e">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.3880000000000017" y="6.222857142857139" z="17.715127801332095"/>
<lineStyle thickness="2" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="a" a1="e"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="492.05526013894786" y="124.98111209433931" z="50.20249502040813"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="F" a1="E"/>
<output a0="高_2"/>
</command>
<element type="segment" label="高_2">
<show object="true" label="true"/>
<condition showObject="h ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-9" y="6"/>
<labelMode val="0"/>
<coords x="3.334765069993336" y="-6.125078699987753" z="-17.43677373150829"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="d"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="10.975599763787171" y="-2.4405979642765128" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="G" a1="c"/>
<output a0="j"/>
</command>
<element type="line" label="j">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.790095238095239" y="0.27657142857142825" z="-84.8259677895692"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="c" a1="j"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="653.2338119611782" y="236.6414269839965" z="60.76207557369615"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="H" a1="G"/>
<output a0="高_1"/>
</command>
<element type="segment" label="高_1">
<show object="true" label="true"/>
<condition showObject="i ≟ 1"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-13" y="14"/>
<labelMode val="0"/>
<coords x="6.3351559554198955" y="0.22491677948236166" z="-68.98320477372522"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="h">
<value val="1.0"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="80" y="-5"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="100.0" x="147.0" y="77.0" fixed="true" horizontal="true"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="i">
<value val="1.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="100.0" x="147.0" y="110.0" fixed="true" horizontal="true"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>