Parallelogram Variations: Exploring Squares, Rectangles, and Rhombuses
2013-06-17 12:49
This interactive applet demonstrates how a general parallelogram can dynamically transform into special parallelograms, including squares, rectangles, and rhombuses. By manipulating vectors, segments, and angles, users can visually explore the geometric properties and hierarchical relationships among these quadrilaterals. It is an excellent educational tool for understanding the definitions and co
In collections
我的第一个绘本
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="0761b695-228b-48db-90b2-4b1fb6cbc554" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="807" height="675" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.8971499380421314" orientation="1" />
</panes>
<views>
<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="1" visible="true" inframe="false" stylebar="false" location="1" size="805" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="724" window="100,100,250,400" />
<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="false" 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 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
<input show="true" cmd="true" top="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="16"/>
<graphicsSettings javaLatexFonts="false"/>
<consProtColumns col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
<size width="805" height="511"/>
<coordSystem xZero="214.99999999999997" yZero="315.00000000000006" scale="49.999999999999986" yscale="50.00000000000002"/>
<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"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label="text1" exp=""你觀察到什麼？可以試著拉動A、B兩點。 說說看！""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="16" style="0"/>
<startPoint x="-1.96" y="-1.1" z="1.0"/>
</element>
<element type="point" label="O">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-6" y="32"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.78" y="2.82" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-38" y="14"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-0.46" y="1.12" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="A"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="1.6999999999999997" y="-2.24" z="3.2908"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Vector">
<input a0="A" a1="O"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.24" y="1.6999999999999997" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="A"/>
</element>
<command name="Translate">
<input a0="O" a1="u"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0200000000000005" y="4.52" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="C"/>
<output a0="b"/>
</command>
<element type="segment" 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="-1.6999999999999997" y="2.24" z="-3.2908000000000026"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="16" y="20"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.48" y="0.58" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="B" a1="O"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.7" y="2.2399999999999998" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="B"/>
</element>
<command name="Translate">
<input a0="O" a1="v"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-16" y="-6"/>
<labelMode val="0"/>
<coords x="0.08000000000000007" y="5.06" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="B"/>
<output a0="c"/>
</command>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-29" y="-6"/>
<labelMode val="2"/>
<coords x="4.4799999999999995" y="3.4" z="-17.5624"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="D" a1="A"/>
<output a0="d"/>
</command>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="153" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.9399999999999995" y="-0.54" z="2.4172"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="e"/>
</command>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="153" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5400000000000001" y="3.94" z="-4.1644000000000005"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="153" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.9399999999999995" y="0.5400000000000005" z="13.397999999999998"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="153" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.54" y="-3.9400000000000004" z="19.9796"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="C" a1="O" a2="D"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<value val="1.5707963267948968"/>
<show object="true" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-10" y="-29"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<arcSize val="30"/>
<allowReflexAngle val="true"/>
</element>
<command name="Angle">
<input a0="B" a1="O" a2="C"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<value val="1.5707963267948966"/>
<show object="true" label="true"/>
<objColor r="255" g="153" b="51" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="29" y="9"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<arcSize val="30"/>
<allowReflexAngle val="true"/>
</element>
<command name="Distance">
<input a0="a" a1="c"/>
<output a0="h"/>
</command>
<element type="numeric" label="h">
<value val="0.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Distance">
<input a0="D" a1="O"/>
<output a0="distanceDO"/>
</command>
<element type="numeric" label="distanceDO">
<value val="2.812045518834999"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="文字DO" exp=""\overline{" + (Name[D]) + (Name[O]) + "} \, = \, " + distanceDO" />
<element type="text" label="文字DO">
<show object="true" label="false"/>
<objColor r="51" g="51" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" size="0" style="0"/>
<startPoint exp="Midpoint[D, O]"/>
<labelOffset x="-45" y="-29"/>
</element>
<command name="Distance">
<input a0="A" a1="O"/>
<output a0="distanceAO"/>
</command>
<element type="numeric" label="distanceAO">
<value val="2.8120455188349993"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="文字AO" exp=""\overline{" + (Name[A]) + (Name[O]) + "} \, = \, " + distanceAO" />
<element type="text" label="文字AO">
<show object="true" label="false"/>
<objColor r="0" g="153" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" size="0" style="0"/>
<startPoint exp="Midpoint[A, O]"/>
<labelOffset x="-36" y="-19"/>
</element>
</construction>
</geogebra>