Comparing Angle Sizes Using a Protractor
2019-01-03 00:50
This GeoGebra applet demonstrates how to use a protractor to visually compare the sizes of two or more angles. By constructing segments and angles (e.g., α, β) and applying the Rotate command to dynamically adjust angle measures, a protractor image is overlaid for measurement. The applet helps students understand angle measurement and comparison, making it suitable for elementary or middle school
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.518.0" app="classic" platform="w" id="3078201d-a13b-4675-baa1-3c309b853e45" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1432" height="460" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.13966480446927373" 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 | 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 , 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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="380" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1430" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="200" window="100,100,600,400" />
<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="false" stylebar="false" location="1" size="150" 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="150" 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="false" items="0 39 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="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1430" height="458"/>
<coordSystem xZero="219.00000000000003" yZero="415.99999999999994" scale="49.99999999999998" yscale="49.99999999999999"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0"/>
<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>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1" y="0" z="1"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="B" exp="A + (4, 0)" type="point" />
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<algebra labelVisible="false"/> <coords x="3" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="B" a1="73°" a2="A"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.16948681889094708" y="3.8252190238521417" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="B" a1="A" a2="B'"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="1.2740903539558606"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="25" y="-5"/>
<labelMode val="3"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<caption val="A"/>
</element>
<command name="Segment">
<input a0="B'" a1="A"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.8252190238521417" y="-1.169486818890947" z="3.8252190238521417"/>
<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="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="4" z="0"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="6" y="0" z="1"/>
<pointSize val="7"/>
<pointStyle val="3"/>
</element>
<expression label="D" exp="C + (4, 0)" type="point" />
<element type="point" label="D">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="10" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="D" a1="75°" a2="C"/>
<output a0="D'"/>
</command>
<element type="point" label="D'">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.035276180410083" y="3.8637033051562732" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="D" a1="C" a2="D'"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<angleStyle val="0"/>
<value val="1.3089969389957472"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="21" y="-7"/>
<labelMode val="3"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<caption val="B"/>
</element>
<command name="Segment">
<input a0="D'" a1="C"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.8637033051562732" y="-1.035276180410083" z="-23.18221983093764"/>
<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="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="4" z="0"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="E">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="13" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="false" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="22" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="6c4eadc16e048af21063d94598618bb4/protractor.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="E"/>
<startPoint number="1" exp="F"/>
<show object="true" label="true"/>
<condition showObject="a ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="boolean" label="a">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="923" y="97"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="顯示量度器"/>
</element>
<expression label="text1" exp=""比較以下兩角的大小：""/>
<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="4" size="36" style="1"/>
<startPoint x="-1.94" y="6.46" z="1"/>
</element>
</construction>
</geogebra>