Quadrilateral Classification: Dynamic Geometry Based on Side Lengths and Angle P
2011-09-28 07:48
This GeoGebra example demonstrates how to classify quadrilaterals based on side length relationships, right angles, and parallel sides. It covers identification conditions for special quadrilaterals including parallelograms, rectangles, rhombuses, and squares. Using geometric construction commands such as rotation, reflection, intersection, and circular arcs, combined with conditional logic and dy
In collections
Quadrilaterals (2001 Old Curriculum Teacher Edition)
4th Grade Quadrilaterals (Student Edition)
Quadrilaterals: Interactive Geometry
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<command name="If">
<input a0="γ ≟ 90° ∨ α ≟ γ ∨ β ≟ γ ∨ δ ≟ γ" a1="true" a2="false"/>
<output a0="show_γ"/>
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<element type="boolean" label="show_γ">
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<command name="If">
<input a0="δ ≟ 90° ∨ δ ≟ β ∨ δ ≟ γ ∨ α ≟ δ" a1="true" a2="false"/>
<output a0="show_δ"/>
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<element type="boolean" label="show_δ">
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<checkbox fixed="true"/>
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<command name="Segment">
<input a0="Midpoint[c'] - (0.001 * UnitVector[Vector[H, G]])" a1="Midpoint[c']"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false"/>
<condition showObject="α + β ≟ 180° ∧ parallel ∧ joinredpoints"/>
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<labelMode val="0"/>
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<coords x="NaN" y="NaN" z="NaN"/>
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<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
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<command name="Segment">
<input a0="Midpoint[a'] - (0.001 * UnitVector[Vector[E, F]])" a1="Midpoint[a']"/>
<output a0="r"/>
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<element type="segment" label="r">
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<condition showObject="α + β ≟ 180° ∧ parallel ∧ joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<command name="Segment">
<input a0="Midpoint[b'] - (0.001 * UnitVector[Vector[F, G]])" a1="Midpoint[b']"/>
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<show object="true" label="false"/>
<condition showObject="α + δ ≟ 180° ∧ parallel ∧ joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<keepTypeOnTransform val="true"/>
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<command name="Segment">
<input a0="Midpoint[d'] - (0.001 * UnitVector[Vector[E, H]])" a1="Midpoint[d']"/>
<output a0="t_1"/>
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<element type="segment" label="t_1">
<show object="true" label="false"/>
<condition showObject="α + δ ≟ 180° ∧ parallel ∧ joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<decoration type="5"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
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<keepTypeOnTransform val="true"/>
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<element type="boolean" label="equalangles">
<value val="false"/>
<show object="true" label="true"/>
<condition showObject="joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="32" y="160"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="顯示直角和相等角"/>
</element>
<element type="boolean" label="parallel">
<value val="false"/>
<show object="true" label="true"/>
<condition showObject="joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="33" y="217"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="顯示平行邊"/>
</element>
<command name="Segment">
<input a0="G" a1="L"/>
<output a0="g_1"/>
</command>
<element type="segment" label="g_1">
<show object="true" label="false"/>
<condition showObject="joinredpoints ≟ false"/>
<objColor r="255" g="0" b="255" alpha="0" dynamicr="If[c ≟ b ∧ (b ≠ a), 0, 1]" dynamicg="0" dynamicb="If[c ≟ b ∧ (b ≠ a), 1, If[c ≟ a, 0, 1]]" colorSpace="0"/>
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<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
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<element type="boolean" label="joinredpoints">
<value val="false"/>
<show object="true" label="true"/>
<condition showObject="close ≟ true ∧ (¬joinredpoints)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="567" y="54"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="連接紅點"/>
</element>
<command name="If">
<input a0="Distance[L, M] < dist" a1="true" a2="false"/>
<output a0="close"/>
</command>
<element type="boolean" label="close">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
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<command name="Segment">
<input a0="E" a1="M"/>
<output a0="l_1"/>
</command>
<element type="segment" label="l_1">
<show object="true" label="false"/>
<condition showObject="joinredpoints ≟ false"/>
<objColor r="0" g="204" b="204" alpha="0" dynamicr="If[d ≟ c ∧ (c ≠ b) ∧ (c ≠ a), 1, If[d ≟ b ∧ (b ≠ a), 0, If[d ≟ a, 1, 0]]]" dynamicg="If[d ≟ c ∧ (c ≠ b) ∧ (c ≠ a), 0, If[d ≟ b ∧ (b ≠ a), 0, If[d ≟ a, 0, 0.8]]]" dynamicb="If[d ≟ c ∧ (c ≠ b) ∧ (c ≠ a), 1, If[d ≟ b ∧ (b ≠ a), 1, If[d ≟ a, 0, 0.8]]]" colorSpace="0"/>
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<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""電子幾何條""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="8" style="1"/>
<absoluteScreenLocation x="11" y="34"/>
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<expression label="text2" exp=""拖拉綠色及紅色 ● 點，將紅點重疊，再按「連接紅點」鈕連成一個四邊形。 拖拉 × 點，改變四邊長度。""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<condition showObject="¬joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="201" y="26"/>
</element>
<expression label="text3" exp=""拖拉綠色 ● 點，觀察四邊形的變化。 拖拉黃色 ● 點轉動四邊形。拖拉 × 點，改變四邊長度。 拖拉淺黃色部分移動四邊形。""/>
<element type="text" label="text3">
<show object="true" label="false"/>
<condition showObject="joinredpoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="201" y="25"/>
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</construction>
</geogebra>