Geometric Construction and Properties of Parallelograms
2016-10-22 06:56
This GeoGebra applet demonstrates the geometric construction and properties of parallelograms. Using commands like Intersect, Polygon, Midpoint, and Rotate, it dynamically illustrates the generation of parallelograms and derived figures. Ideal for geometry education, this interactive tool helps students visually understand side-angle relationships, diagonal bisection, and rotational symmetry, serv
In collections
Polygons: Interactive GeoGebra Geometry Book
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.60.0" id="16cb889a-1d92-4007-a1eb-148fbae20ba8" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="744" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1447178002894356" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="548,298,700,550" />
<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="1355" 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="1355" height="578"/>
<coordSystem xZero="269.66666666666674" yZero="488.6666666666665" scale="33.333333333333314" yscale="33.33333333333326"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<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="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="" author="" date="">
<element type="numeric" label="a">
<value val="9.5"/>
<show object="true" label="true"/>
<objColor r="128" g="0" b="128" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="3" max="15" absoluteScreenLocation="true" width="100.0" x="196.0" y="37.0" fixed="true" horizontal="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="5.4"/>
<show object="true" label="true"/>
<objColor r="204" g="102" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="10" absoluteScreenLocation="true" width="100.0" x="344.0" y="38.0" fixed="true" horizontal="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label="A" exp="(a, 0)" type="point" />
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.5" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="(0, b)" type="point" />
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="D" exp="(a, b)" type="point" />
<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="9.5" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="C" a1="A" a2="D" a3="B"/>
<output a0="poly1" a1="c" a2="a_1" a3="d" a4="b_1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m < 1"/>
<objColor r="255" g="255" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.0" y="9.5" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a_1">
<show object="true" label="false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-5.4" y="0.0" z="51.300000000000004"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-9.5" z="51.300000000000004"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_1">
<show object="true" label="false"/>
<objColor r="255" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.4" y="0.0" z="-0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Midpoint">
<input a0="C" a1="B"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="2.7" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="B" a1="D"/>
<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="4.75" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="D" a1="A"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.5" y="2.7" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Midpoint">
<input a0="A" a1="C"/>
<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="4.75" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="B" a1="H"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.4" y="4.75" z="-25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="F"/>
<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="-5.4" y="-4.75" z="51.300000000000004"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="D"/>
<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="-2.7" y="9.5" z="-25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="C"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.7" y="-9.5" z="-0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="g" a1="f"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="365.51250000000005" y="277.02000000000004" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="g" a1="e"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="121.8375" y="207.76500000000004" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="e" a1="h"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="243.675" y="69.25500000000001" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="h" a1="f"/>
<output a0="L"/>
</command>
<element type="point" label="L">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="487.35" y="138.51000000000002" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="I" a1="J" a2="K" a3="L"/>
<output a0="poly2" a1="i" a2="j" a3="k" a4="l"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="i">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0799999999999996" y="-3.8000000000000007" z="10.260000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.1600000000000006" y="1.9000000000000001" z="-10.260000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="3.8000000000000003" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.16" y="-1.8999999999999995" z="20.520000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="G" a1="L" a2="A"/>
<output a0="poly3" a1="a_2" a2="g_1" a3="l_1"/>
</command>
<element type="polygon" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a_2">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.54" y="-1.8999999999999995" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.16" y="1.8999999999999995" z="-20.520000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.7" y="0.0" z="25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="D" a1="I" a2="F"/>
<output a0="poly4" a1="f_1" a2="d_1" a3="i_1"/>
</command>
<element type="polygon" label="poly4">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.799999999999999" z="10.259999999999998"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="-0.9500000000000011" z="10.260000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.75" z="-25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="J" a1="E" a2="B"/>
<output a0="poly5" a1="b_2" a2="j_1" a3="e_1"/>
</command>
<element type="polygon" label="poly5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="b_2">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5400000000000005" y="-1.9000000000000001" z="5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.7" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.1599999999999997" y="1.9000000000000001" z="-10.260000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="H" a1="K" a2="C"/>
<output a0="poly6" a1="c_1" a2="h_1" a3="k_1"/>
</command>
<element type="polygon" label="poly6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="-0.9499999999999997" z="5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.8000000000000003" z="-0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.0" y="4.75" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="m">
<value val="0.0"/>
<show object="true" label="true"/>
<objColor r="51" g="255" b="204" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="100.0" x="502.0" y="37.0" fixed="true" horizontal="true"/>
<lineStyle thickness="13" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="Rotate">
<input a0="G" a1="(180 * m)°" a2="G"/>
<output a0="G'"/>
</command>
<element type="point" label="G'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.5" y="2.7" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="L" a1="(180 * m)°" a2="G"/>
<output a0="L'"/>
</command>
<element type="point" label="L'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="487.35" y="138.51000000000002" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="A" a1="(180 * m)°" a2="G"/>
<output a0="A'"/>
</command>
<element type="point" label="A'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="9.5" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="G'" a1="L'" a2="A'"/>
<output a0="poly3'" a1="a'" a2="g'" a3="l'"/>
</command>
<element type="polygon" label="poly3'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m > 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.54" y="-1.8999999999999995" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.16" y="1.8999999999999995" z="-20.520000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.7" y="0.0" z="25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="D" a1="(180 * m)°" a2="F"/>
<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="9.5" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="I" a1="(180 * m)°" a2="F"/>
<output a0="I'"/>
</command>
<element type="point" label="I'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="365.51250000000005" y="277.02000000000004" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="F" a1="(180 * m)°" a2="F"/>
<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="4.75" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="D'" a1="I'" a2="F'"/>
<output a0="poly4'" a1="f'" a2="d'" a3="i'"/>
</command>
<element type="polygon" label="poly4'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m > 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.799999999999999" z="10.259999999999998"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="-0.9500000000000011" z="10.260000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.75" z="-25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="J" a1="(180 * m)°" a2="E"/>
<output a0="J'"/>
</command>
<element type="point" label="J'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="121.8375" y="207.76500000000004" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="E" a1="(180 * m)°" a2="E"/>
<output a0="E'"/>
</command>
<element type="point" label="E'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="2.7" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="B" a1="(180 * m)°" a2="E"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="5.4" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="J'" a1="E'" a2="B'"/>
<output a0="poly5'" a1="b'" a2="j'" a3="e'"/>
</command>
<element type="polygon" label="poly5'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m > 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="b'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5400000000000005" y="-1.9000000000000001" z="5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.7" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.1599999999999997" y="1.9000000000000001" z="-10.260000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="H" a1="(180 * m)°" a2="H"/>
<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="4.75" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="K" a1="(180 * m)°" a2="H"/>
<output a0="K'"/>
</command>
<element type="point" label="K'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="243.675" y="69.25500000000001" z="64.125"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="C" a1="(180 * m)°" a2="H"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="H'" a1="K'" a2="C'"/>
<output a0="poly6'" a1="c'" a2="h'" a3="k'"/>
</command>
<element type="polygon" label="poly6'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m > 0"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="-0.9499999999999997" z="5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.8000000000000003" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k'">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.75" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="G" a1="D" a2="I" a3="L"/>
<output a0="poly7" a1="g_2" a2="d_2" a3="i_2" a4="l_2"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 1"/>
<objColor r="0" g="255" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="g_2">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.7" y="0.0" z="25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_2">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.799999999999999" z="10.259999999999998"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_2">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.16" y="1.8999999999999995" z="-20.520000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_2">
<show object="true" label="false"/>
<objColor r="0" g="255" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.54" y="1.8999999999999995" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="L" a1="K" a2="H" a3="A"/>
<output a0="poly8" a1="l_3" a2="k_2" a3="h_2" a4="a_3"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 1"/>
<objColor r="0" g="255" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="l_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="-3.8000000000000003" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.08" y="0.9499999999999997" z="-5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.75" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.16" y="-1.8999999999999995" z="20.520000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="I" a1="F" a2="B" a3="J"/>
<output a0="poly9" a1="i_3" a2="f_2" a3="b_3" a4="j_2"/>
</command>
<element type="polygon" label="poly9">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 1"/>
<objColor r="0" g="255" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="i_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="-0.9500000000000011" z="10.260000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-4.75" z="25.650000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.1599999999999997" y="1.9000000000000001" z="-10.260000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0799999999999996" y="3.8000000000000007" z="-10.260000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="J" a1="E" a2="C" a3="K"/>
<output a0="poly10" a1="j_3" a2="e_2" a3="c_2" a4="k_3"/>
</command>
<element type="polygon" label="poly10">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="m ≟ 1"/>
<objColor r="0" g="255" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="j_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5400000000000005" y="-1.9000000000000001" z="5.130000000000001"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.7" y="0.0" z="-0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.08" y="3.8000000000000003" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_3">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.1600000000000006" y="-1.9000000000000001" z="10.260000000000002"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""紅色平行四邊形面積是長方形面積的幾分之幾？""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<condition showObject="m < 1"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="4.0" size="36" style="1"/>
<startPoint x="-5.270000000000003" y="11.480000000000022" z="1.0"/>
</element>
<expression label="text2" exp=""答：５分之１""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<condition showObject="m ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="4.0" size="36" style="1"/>
<startPoint x="4.659999999999999" y="11.420000000000023" z="1.0"/>
</element>
</construction>
</geogebra>