Geometric Construction and Property Verification of Similar Triangles
2016-07-31 00:34
This GeoGebra example demonstrates the construction and property verification of similar triangles. Using commands such as Intersect, Polygon, Segment, and Angle, multiple triangles (poly1, poly2, poly3) are constructed with corresponding angles labeled (α, β, γ, δ), visually illustrating the core properties of similar triangles: equal corresponding angles and proportional corresponding sides. The
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<coords x="4.66" y="6.4" z="1.0"/>
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<command name="Polygon">
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<output a0="poly1" a1="b" a2="c" a3="a"/>
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<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
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<command name="Intersect">
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<command name="Angle">
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<output a0="α"/>
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<animation step="0.1" speed="1" type="0" playing="false"/>
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<command name="Rotate">
<input a0="B" a1="γ * n" a2="A"/>
<output a0="B'"/>
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<element type="point" label="B'">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
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<command name="Rotate">
<input a0="F" a1="-(n * γ)" a2="A"/>
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<element type="point" label="F'">
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<input a0="F" a1="-γ * n" a2="A"/>
<output a0="G"/>
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<element type="point" label="G">
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<objColor r="125" g="125" b="255" alpha="0.0"/>
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<input a0="A" a1="G" a2="B'"/>
<output a0="poly3" a1="b'" a2="a_2" a3="g_1"/>
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<element type="polygon" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.55"/>
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<command name="Angle">
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<output a0="δ"/>
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<show object="true" label="true"/>
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