2014 Jiangsu Vocational College Entrance Exam Math: Solid Geometry
2019-04-05 04:48
This GeoGebra applet demonstrates a solid geometry problem from the 2014 Jiangsu Province Vocational College Entrance Examination. By constructing a 3D prism model using commands like Point, Segment, and Intersect, it visually illustrates the spatial relationships of faces, edges, and cross-sections. This model helps students understand point-line-plane structures in space, enhancing spatial imagi
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.426.0" app="classic" platform="d" id="c54e9bea-b70b-4dcc-8098-89420f32602b" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1280" height="706" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.15625" orientation="1" />
<pane location="1" divider="0.35078125" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="526,302,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1,3" size="449" 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="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="true" inframe="false" stylebar="true" location="1,1" size="602" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" 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="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="449" height="550"/>
<coordSystem xZero="211.92009281249992" yZero="424.79979984375024" scale="65.15188281249998" yscale="65.15188281249992"/>
<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>
<spreadsheetView>
<prefCellSize height="26"/>
</spreadsheetView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="-0.1635669378499225" yZero="-0.28176793726803195" zZero="-0.9507128500122937" scale="157.59896746459142" xAngle="23.0" zAngle="5686.939046646377"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="2"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<command name="Point">
<input a0="Circle[(1, -1, 0), Distance[(-1, -1, 0), (1, -1, 0)], Segment[(-1, -1, 0), (1, -1, 0)]]"/>
<output a0="A"/>
</command>
<element type="point3d" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="1.0" y="1.0" z="0.0" w="1.0"/>
<pointSize val="5"/>
</element>
<command name="Cube">
<input a0="(-1, -1, 0)" a1="(1, -1, 0)" a2="A"/>
<output a0="a" a1="B" a2="C_1" a3="D_1" a4="A_1" a5="B_1" a6="face1" a7="face3" a8="face2" a9="face4" a10="faceABFE" a11="faceCDEF" a12="edge2" a13="edge1" a14="edge4" a15="edgeAB" a16="edge3" a17="edgeBF" a18="edgeCF" a19="edgeCD" a20="edge5" a21="edgeDE" a22="edgeAE" a23="edgeEF"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="true" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="1.0" z="0.0" w="1.0"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="C_1">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="-1.0" z="2.0" w="1.0"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="D_1">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="-1.0" z="2.0" w="1.0"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="A_1">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="1.0" z="2.0" w="1.0"/>
<pointSize val="4"/>
</element>
<element type="point3d" label="B_1">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="1.0" z="2.0" w="1.0"/>
<pointSize val="4"/>
</element>
<element type="polygon3d" label="face1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="face3">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="face2">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="face4">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceABFE">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="faceCDEF">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="segment3d" label="edge2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge4">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAB">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge3">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeBF">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCF">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeCD">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge5">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeDE">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeAE">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edgeEF">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="edge3" a1="edge1"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="-1.0" z="0.0" w="1.0"/>
<pointSize val="4"/>
</element>
<command name="Intersect">
<input a0="edge5" a1="edge4"/>
<output a0="D"/>
</command>
<element type="point3d" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="-1.0" z="0.0" w="1.0"/>
<pointSize val="4"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="f"/>
</command>
<element type="segment3d" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="C_1"/>
<output a0="g"/>
</command>
<element type="segment3d" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="D_1"/>
<output a0="h"/>
</command>
<element type="segment3d" label="h">
<show object="true" label="true" ev="4"/>
<condition showObject="c"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="D_1"/>
<output a0="i"/>
</command>
<element type="segment3d" label="i">
<show object="true" label="true" ev="4"/>
<condition showObject="b"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""BC_1∥AD_1 所以AC与BC_1所成角\\转化为AC与AD_1所成角""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<condition showObject="c"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint x="-2.340000000000001" y="6.820000000000009" z="1.0"/>
</element>
<expression label="text2" exp=""ΔACD_1各边长为正方形的对角线，\\所以它为等边三角形""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<condition showObject="b"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<startPoint x="-2.320000000000001" y="4.3600000000000065" z="1.0"/>
</element>
<element type="boolean" label="b">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="39" y="147"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="构造三角形"/>
</element>
<element type="boolean" label="c">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="39" y="32"/>
<labelMode val="4"/>
<checkbox fixed="true"/>
<caption val="异面角转化"/>
</element>
</construction>
</geogebra>