Geometric Construction and Properties of a Rhombus
2017-09-27 12:58
This GeoGebra applet demonstrates the geometric construction and fundamental properties of a rhombus. Using commands such as Circle, Intersect, Polygon, and Segment, it dynamically constructs a rhombus and measures its side lengths and interior angles. The interactive model visually illustrates key geometric features, making it an excellent tool for plane geometry education.
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.388.0" app="classic" platform="d" id="e5a950ed-e519-4c87-9840-1a5f9c60e934" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1030" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.10416666666666667" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="985,212,700,550" />
<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 , 22 , 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="1" visible="true" inframe="false" stylebar="true" location="1" size="1891" 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" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 | 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 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="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1891" height="850"/>
<coordSystem xZero="282.1541658039645" yZero="401.12885396645765" scale="50.568133143903935" yscale="50.56813314390404"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" 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" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-27" y="19"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="1.8360542188065376" y="0.0025481258343267106" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<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"/>
<labelOffset x="-7" y="34"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="7.313812300397748" y="-3.06262336386472" z="1.0"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="B"/>
<output a0="c_2"/>
</command>
<element type="conic" label="c_2">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<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="-36.03000827435914" A3="0.0" A4="-1.8360542188065376" A5="-0.0025481258343267106"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="B" a1="A"/>
<output a0="d_2"/>
</command>
<element type="conic" label="d_2">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<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="23.470402372637764" A3="0.0" A4="-7.313812300397748" A5="3.06262336386472"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="c_2" a1="d_2" a2="1"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-7" y="-1"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="7.229449636637309" y="3.2138400354283028" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="C" a1="B"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<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="23.192599960295418" A3="0.0" A4="-7.229449636637309" A5="-3.2138400354283028"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="d_2" a1="e" a2="2"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="5" y="14"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="12.707207718228517" y="0.14866854572925592" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="D" a1="B"/>
<output a0="f"/>
</command>
<element type="conic" label="f">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<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="122.094120468994" A3="0.0" A4="-12.707207718228517" A5="-0.14866854572925592"/>
<eqnStyle style="specific"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="D" a3="C"/>
<output a0="poly1" a1="a_1" a2="b_1" a3="d_1" a4="c_1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0.2800000011920929"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
</element>
<element type="segment" label="a_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<coords x="3.0651714896990465" y="5.47775808159121" z="-5.641779061909349"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="2"/>
<isShape val="false"/>
<auxiliary val="false"/>
<coords x="-3.211291909593976" y="5.393395417830769" z="40.00472508576563"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<coords x="-3.065171489699047" y="-5.477758081591208" z="39.764141139444575"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<auxiliary val="false"/>
<coords x="3.2112919095939763" y="-5.393395417830771" z="-5.882363008230408"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-21" y="-31"/>
<labelMode val="2"/>
<isShape val="false"/>
<coords x="-3.2112919095939763" y="5.393395417830771" z="5.882363008230408"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="D"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-10" y="5"/>
<labelMode val="2"/>
<isShape val="false"/>
<coords x="-3.211291909593976" y="5.393395417830769" z="40.00472508576563"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="204" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-4" y="-36"/>
<labelMode val="2"/>
<isShape val="false"/>
<coords x="3.065171489699047" y="5.477758081591208" z="-39.764141139444575"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="204" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-13" y="3"/>
<labelMode val="2"/>
<isShape val="false"/>
<coords x="3.0651714896990465" y="5.47775808159121" z="-5.641779061909349"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Length">
<input a0="g"/>
<output a0="k"/>
</command>
<element type="numeric" label="k">
<value val="6.277030337803193"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="text2" exp=""AB：" + k + "cm"" />
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<condition showObject="text1"/>
<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="1"/>
<startPoint x="18.229777863713082" y="5.2825532080901025" z="1.0"/>
</element>
<expression label="text4" exp=""BD：" + k + "cm"" />
<element type="text" label="text4">
<show object="true" label="true" ev="40"/>
<condition showObject="text1"/>
<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="1"/>
<startPoint x="18.26932846358017" y="4.451990610881328" z="1.0"/>
</element>
<expression label="text1_1" exp=""CA：" + k + "cm"" />
<element type="text" label="text1_1">
<show object="true" label="true" ev="8"/>
<condition showObject="text1"/>
<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="1"/>
<startPoint x="18.272377138593054" y="2.7685419906959137" z="1.0"/>
</element>
<expression label="text3" exp=""DC：" + k + "cm"" />
<element type="text" label="text3">
<show object="true" label="true" ev="8"/>
<condition showObject="text1"/>
<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="1"/>
<startPoint x="18.26932846358017" y="3.5621021138719273" z="1.0"/>
</element>
<element type="boolean" label="text1">
<value val="true"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="1195" y="46"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text5" exp=""顯示邊長""/>
<element type="text" label="text5">
<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="1"/>
<startPoint x="18.981239261187692" y="6.528397103903264" z="1.0"/>
</element>
<command name="Angle">
<input a0="B" a1="A" a2="C"/>
<output a0="a"/>
</command>
<element type="angle" label="a">
<angleStyle val="0"/>
<value val="1.0471975511965976"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.20999999344348907"/>
<layer val="0"/>
<labelOffset x="30" y="-5"/>
<labelMode val="0"/>
<lineStyle thickness="6" type="0" typeHidden="2" opacity="178"/>
<arcSize val="50"/>
</element>
<command name="Angle">
<input a0="C" a1="D" a2="B"/>
<output a0="d"/>
</command>
<element type="angle" label="d">
<angleStyle val="0"/>
<value val="1.047197551196598"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-39" y="-2"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="50"/>
</element>
<command name="Angle">
<input a0="D" a1="B" a2="A"/>
<output a0="b"/>
</command>
<element type="angle" label="b">
<angleStyle val="0"/>
<value val="2.0943951023931957"/>
<show object="true" label="true" ev="4"/>
<objColor r="127" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="0" y="-40"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="50"/>
</element>
<command name="Angle">
<input a0="A" a1="C" a2="D"/>
<output a0="c"/>
</command>
<element type="angle" label="c">
<angleStyle val="0"/>
<value val="2.0943951023931953"/>
<show object="true" label="true" ev="4"/>
<objColor r="127" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="1" y="32"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="50"/>
</element>
</construction>
</geogebra>