Geometric Construction: Angle Bisector
2020-12-26 02:39
This example demonstrates the compass-and-straightedge construction of an angle bisector. Using GeoGebra tools like circles and arcs, it shows how to draw an arc from the vertex to intersect both sides, then draw equal-radius arcs from these points. The line connecting the vertex to their intersection forms the bisector, clarifying core geometric construction principles.
In collections
Points, Lines, and Angles
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<element type="point" label="M">
<show object="true" label="true" ev="4"/>
<condition showObject="t ≥ 3"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-14" y="-6"/>
<labelMode val="3"/>
<caption val="$\large %n$"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Segment">
<input a0="M_2" a1="C"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 2"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<startStyle val="default"/>
<endStyle val="default"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Segment">
<input a0="H'" a1="C"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 2"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<startStyle val="default"/>
<endStyle val="default"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Segment">
<input a0="M_3" a1="D"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 3"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<startStyle val="default"/>
<endStyle val="default"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Intersect">
<input a0="Circle[O, 20]" a1="Ray[O, M]"/>
<output a0="K" a1=""/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Point">
<input a0="Segment[O, K]"/>
<output a0="M_4"/>
</command>
<element type="point" label="M_4">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="21" y="4"/>
<labelMode val="0"/>
<animation step="0.1" speed="10" type="3" playing="false"/>
<pointSize val="1"/>
<pointStyle val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<command name="Segment">
<input a0="O" a1="M_4"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="8" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<startStyle val="default"/>
<endStyle val="default"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
<element type="numeric" label="t">
<value val="0"/>
<slider min="0" max="4" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="83" y="352"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,1]
StartAnimation[M_1,true]"/>
<caption val="1、以O为圆心画弧"/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="83" y="395"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,2]
SetValue[M_2,H']
StartAnimation[M_2,true]"/>
<caption val="2、以C为圆心画弧"/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="83" y="439"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,3]
SetValue[M_3,J]
StartAnimation[M_3,true]"/>
<caption val="3、以D为圆心，同样长为半径画弧"/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<element type="button" label="button4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="84" y="482"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t,4]
StartAnimation[M_4,true]"/>
<caption val="4、作射线OM"/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<element type="button" label="button5">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="83" y="307"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[M_4,O]
SetValue[M_3,J]
SetValue[M_2,H']
SetValue[M_1,E_1]
SetValue[t,0]


"/>
<caption val="复位"/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<command name="Segment">
<input a0="D" a1="J"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="true" label="false" ev="4"/>
<condition showObject="t ≟ 3"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="8" type="15" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<startStyle val="default"/>
<endStyle val="default"/>
<coords x="NaN" y="NaN" z="NaN"/>
</element>
</construction>
</geogebra>