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451 lines
22 KiB
HTML
451 lines
22 KiB
HTML
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<h1 class="center">Geometry</h1>
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<p class="center">Geometry is all about <b>shapes</b> and their properties.</p>
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<p class="center larger">If you like playing with objects, or like drawing, then geometry is for you!</p>
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<p>Geometry can be divided into:</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/plane.svg" alt="plane" height="109" width="250"></p>
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<p><br>
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<b><a href="plane-geometry.html">Plane Geometry</a></b> is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper</p>
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<div style="clear:both"></div>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/3d-shapes.jpg" alt="3d shapes" height="136" width="200"></p>
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<p><br>
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<b><a href="solid-geometry.html">Solid Geometry</a></b> is about three dimensional objects like cubes, prisms, cylinders and spheres.</p>
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<div style="clear:both"></div>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="../images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td style="text-align:center;"><i>Hint: Try drawing some of the shapes and angles as you learn ... it helps.</i></td>
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</tr>
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</tbody></table>
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<h2>Point, Line, Plane and Solid</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="dimensions.html"><img src="images/dimensions.svg" alt="dimensions" height="148" width="305"></a></p>
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<p>A <a href="point.html">Point</a> has no <a href="dimensions.html">dimensions</a>, only position<br>
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A <a href="line.html">Line</a> is one-dimensional<br>
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A <a href="plane.html">Plane</a> is two dimensional (2D)<br>
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A <a href="solid-geometry.html">Solid</a> is three-dimensional (3D)</p>
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<div style="clear:both"></div>
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<h2>Why?</h2>
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<p>Why do we do Geometry? To discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.</p>
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<h2>Plane Geometry</h2>
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<p><a href="plane-geometry.html">Plane Geometry</a> is all about shapes on a flat surface (like on an endless piece of paper).</p>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="pentagon.html"><img src="images/pentagon-regular.svg" alt="Regular Pentagon" height="100" width="110"></a></p>
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<ul class="large">
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<li><a href="../shape.html">2D Shapes</a></li>
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<li><a href="../activity/shapes-sorting.html"><img src="../images/style/activity-small.svg" alt="activity" height="30" width="41"> Activity: Sorting Shapes</a></li>
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<li><a href="../triangle.html">Triangles</a></li>
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<li><a href="../right_angle_triangle.html">Right Angled Triangles</a></li>
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<li><a href="triangles-interactive.html">Interactive Triangles</a></li>
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</ul>
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<p> </p>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="kite.html"><img src="images/kite.svg" alt="kite" height="181" width="130"></a></p>
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<ul class="large">
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<li><a href="../quadrilaterals.html">Quadrilaterals (Rhombus, Parallelogram,
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etc)</a></li>
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<li><a href="rectangle.html">Rectangle</a>, <a href="rhombus.html">Rhombus</a>, <a href="square.html">Square</a>, <a href="parallelogram.html">Parallelogram</a>, <a href="trapezoid.html">Trapezoid</a> and <a href="kite.html">Kite</a></li>
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<li><a href="quadrilaterals-interactive.html">Interactive Quadrilaterals</a></li>
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<li><a href="parallelogram-in-quadrilateral.html">Parallelogram In Any Quadrilateral</a></li>
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<li><a href="paper-sizes.html">Paper Sizes</a></li>
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<li><a href="../algebra/shapes-freeplay.html">Shapes Freeplay</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="perimeter.html">Perimeter</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="area.html">Area</a></li>
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<li><a href="../area.html">Area of Plane Shapes</a></li>
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<li><a href="../area-calculation-tool.html">Area Calculation Tool</a></li>
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<li><a href="area-polygon-drawing.html">Area of Polygon by Drawing</a></li>
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<li><a href="../activity/garden-area.html"><img src="../images/style/activity-small.svg" alt="activity" height="30" width="41">Activity: Garden Area</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="drawing.html">General Drawing Tool</a></li>
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<li><a href="square-calc.html">Square Calculator</a> and <a href="rectangle-calc.html">Rectangle Calculator</a></li>
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</ul>
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<h3>Polygons</h3>
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<p>A <a href="polygons.html">Polygon</a> is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.</p>
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<p>Here are some more:</p>
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<div style="float:left; width:200px;">
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<table style="border: 0;">
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<tbody>
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<tr>
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<td>
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<a href="pentagon.html"><img src="images/pentagon-regular.svg" alt="Pentagon" height="100" width="110"></a>
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</td>
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<td><a href="pentagon.html">Pentagon</a></td>
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</tr>
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</tbody></table>
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</div>
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<div style="float:left; width:200px;">
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<table style="border: 0;">
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<tbody>
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<tr>
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<a href="pentagram.html"><img src="images/pentagram-pentagon.svg" alt="Pentagram" height="108" width="114"></a>
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</td>
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<td><a href="pentagram.html">Pentagram</a></td>
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</tr>
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</tbody></table>
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</div>
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<div style="float:left; width:200px;">
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<table style="border: 0;">
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<tbody>
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<tr>
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<td>
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<a href="pentagon.html"><img src="images/hexagon-regular.svg" alt="Hexagon" height="100" width="110"></a>
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</td>
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<td><a href="hexagon.html">Hexagon</a></td>
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</tr>
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</tbody></table>
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</div>
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<div style="clear:both"></div>
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<p> </p>
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<ul class="large">
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<li><a href="regular-polygons.html">Properties of Regular Polygons</a></li>
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<li><a href="polygons-diagonals.html">Diagonals of Polygons</a></li>
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<li><a href="polygons-interactive.html">Interactive Polygons</a></li>
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</ul>
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<p> </p>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="../numbers/pi.html"><img src="../numbers/images/pi-dia.svg" alt="pi circle diameter" height="202" width="179"></a></p>
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<h3>The Circle</h3>
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<ul class="large">
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<li><a href="circle.html">Circle</a></li>
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<li><a href="../numbers/pi.html">Pi</a></li>
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<li><a href="circle-area-lines.html">Circle Area by Lines</a></li>
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<li><a href="circle-sector-segment.html">Circle Sector and Segment</a></li>
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<li><a href="circle-area-by-sectors.html">Circle Area by Sectors</a></li>
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<li><a href="../activity/coin-grid.html"><img src="../images/style/activity-small.svg" alt="activity" height="30" width="41">Activity: Dropping a Coin onto a Grid</a></li>
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<li><a href="arc.html">Arc</a></li>
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<li><a href="annulus.html">Annulus</a></li>
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</ul>
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<p><a href="circle-theorems.html">Circle Theorems</a> (Advanced Topic)</p>
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<p> </p>
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<h3>Symbols</h3>
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<p>There are many special symbols used in Geometry. Here is a short reference for you:</p>
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<p class="center"><a href="symbols.html">Geometric Symbols</a></p>
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<p> </p>
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<h3>Congruent and Similar</h3>
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<ul class="large">
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<li><a href="congruent.html">Congruent Shapes</a></li>
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<li><a href="similar.html">Similar Shapes</a></li>
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</ul>
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<p> </p>
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<h3>Angles</h3>
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<p class="center"><a href="../angles.html">Types of Angles</a><br>
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<img src="images/angle-types.svg" alt="angles" height="83" width="527"></p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td width="16%"><a href="../acute.html">Acute Angles</a></td>
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<td width="16%"><a href="../rightangle.html">Right Angles</a></td>
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<td width="16%"><a href="../obtuse.html">Obtuse Angles</a></td>
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<td width="16%"><a href="straight-angle.html">Straight Angle</a></td>
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<td width="16%"><a href="../reflex.html">Reflex Angles</a></td>
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<td width="16%"><a href="full-rotation.html">Full Rotation</a></td>
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</tr>
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</tbody></table>
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</div><br>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>
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<ul class="large">
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<li><a href="degrees.html">Degrees (Angle)</a></li>
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<li><a href="radians.html">Radians</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="congruent-angles.html">Congruent Angles</a></li>
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<li><a href="parallel-lines.html">Parallel Lines and Pairs of Angles</a></li>
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<li><a href="transversal.html">Transversal</a></li>
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<li><a href="adjacent-angles.html">Adjacent Angles</a></li>
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<li><a href="../proof180deg.html">A Triangle Has 180°</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="supplementary-angles.html">Supplementary Angles</a></li>
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<li><a href="complementary-angles.html">Complementary Angles</a></li>
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</ul>
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</td>
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<td>
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<ul class="large">
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<li><a href="../angle360.html">Angles Around a Point</a></li>
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<li><a href="../angle180.html">Angles on a Straight Line</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="interior-angles.html">Interior Angles</a></li>
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<li><a href="exterior-angles.html">Exterior Angles</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="interior-angles-polygons.html">Interior Angles of Polygons</a></li>
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<li><a href="exterior-angles-polygons.html">Exterior Angles of Polygons</a></li>
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</ul>
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</td>
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</tr>
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</tbody></table>
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<h3>Using Drafting Tools</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/protractor-sm.svg" alt="protractor" height="158" width="274"></p>
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<ul class="large">
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<li><a href="constructions.html">Geometric Constructions</a></li>
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<li><a href="protractor-using.html">Using the Protractor</a></li>
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<li><a href="construct-ruler-triangle.html">Using the Drafting Triangle and Ruler</a></li>
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<li><a href="construct-ruler-compass-1.html">Using a Ruler and Compass</a></li></ul>
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<p> </p>
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<h3>Transformations and Symmetry</h3>
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<p><a href="transformations.html">Transformations</a>:</p>
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<ul class="large">
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<li><a href="rotation.html">Rotation</a></li>
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<li><a href="reflection.html"> Reflection</a></li>
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<li><a href="translation.html">Translation</a></li>
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<li><a href="resizing.html">Resizing</a></li>
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</ul>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/symmetry-art-x.gif" alt="symmetry drawing" height="151" width="151"></p>
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<p><a href="symmetry.html">Symmetry</a>:</p>
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<ul class="large">
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<li><a href="symmetry-reflection.html">Reflection Symmetry</a></li>
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<li><a href="symmetry-rotational.html">Rotational Symmetry</a></li>
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<li><a href="symmetry-point.html">Point Symmetry</a></li>
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<li><a href="symmetry-line-plane-shapes.html">Lines of Symmetry of Plane Shapes</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="symmetry-artist.html">Symmetry Artist</a></li>
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</ul><br>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../images/style/activity-div.svg" alt="Activity" height="78" width="105"></p>
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<ul class="large">
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<li><a href="../activity/shapes-symmetry.html">Activity: Symmetry of Shapes</a></li>
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<li><a href="../activity/mandala.html">Activity: Make a Mandala</a></li>
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<li><a href="../activity/coloring.html">Activity: Coloring (The Four Color
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Theorem)</a></li>
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</ul><br>
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<ul class="large">
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<li><a href="tessellation.html">Tessellations</a></li>
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<li><a href="tessellation-artist.html">Tessellation Artist</a></li>
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</ul>
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<p> </p>
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<h3>Coordinates</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><a href="../data/cartesian-coordinates-interactive.html"><img src="../data/images/interactive-cartesian-coordinates.gif" alt="interactive-cartesian-coordinates" height="150" width="150"></a></p>
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<ul class="large">
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<li><a href="../data/cartesian-coordinates.html">Cartesian Coordinates</a></li>
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<li><a href="../data/cartesian-coordinates-interactive.html">Interactive Cartesian Coordinates</a></li>
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<li><a href="../data/click-coordinate.html">Hit the Coordinate Game</a></li>
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</ul>
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<p> </p>
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<p> </p>
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<h2>More Advanced Topics in Plane Geometry</h2>
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<h3>Pythagoras</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/triangle-abc.svg" alt="abc triangle" height="109" width="189"></p>
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<ul class="large">
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<li><a href="../pythagoras.html">Pythagoras' Theorem</a></li>
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<li><a href="../pythagorean_triples.html">Pythagorean Triples</a></li>
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</ul>
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<p> </p>
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|
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|
<h3>Conic Sections</h3>
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|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/ellipse-draw-3.jpg" alt="ellipse draw 3" height="139" width="180"></p>
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<ul class="large">
|
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<li><a href="../sets/set-of-points.html">Set of all points</a></li>
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|
<li><a href="conic-sections.html">Conic Sections</a></li>
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|
<li><a href="eccentricity.html">Eccentricity</a></li>
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<li><a href="ellipse.html">Ellipse</a></li>
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<li><a href="parabola.html">Parabola</a> and <a href="projectile-animation.html">Projectile Animation</a></li>
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<li><a href="hyperbola.html">Hyperbola</a></li>
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</ul><p> </p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/circle-lines.svg" alt="circle lines" height="208" width="210"></p>
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|
|
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<h3>Circle Theorems</h3>
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<ul class="large">
|
|
<li><a href="circle-theorems.html">Circle Theorems</a></li>
|
|
<li><a href="tangent-secant-lines.html">Tangent and Secant Lines</a></li>
|
|
<li><a href="circle-intersect-secants-line.html">Intersecting Secants Theorem</a></li>
|
|
<li><a href="circle-intersect-chords.html">Intersecting Chords Theorem</a></li>
|
|
<li><a href="circle-intersect-secants-angle.html">Angle of Intersecting Secants Theorem</a></li>
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</ul>
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<p><a href="triangle-centers.html">Triangle Centers</a></p>
|
|
|
|
|
|
<h2>Trigonometry</h2>
|
|
|
|
<p style="float:right; margin: 0 0 5px 10px;"><img src="../algebra/images/adjacent-opposite-hypotenuse.svg" alt="triangle showing Opposite, Adjacent and Hypotenuse" height="190" width="326"></p>
|
|
<p>Trigonometry is a special subject of its own, so you might like to visit:</p>
|
|
<ul class="large">
|
|
<li><a href="../algebra/trigonometry.html">Introduction to Trigonometry</a></li>
|
|
<li><a href="../algebra/trigonometry-index.html">Trigonometry Index</a></li>
|
|
</ul>
|
|
<p> </p>
|
|
|
|
|
|
<h2>Solid Geometry</h2>
|
|
|
|
<p><a href="solid-geometry.html">Solid Geometry</a> is the geometry of three-dimensional space - the kind of space we live in ...</p>
|
|
<p class="center">... let us start with some of the simplest shapes:</p>
|
|
<p class="center"><a href="common-3d-shapes.html"><img src="images/blue-shapes-thumb.jpg" alt="shapes thumbnail" height="91" width="192"><br>
|
|
Common 3D Shapes</a></p>
|
|
|
|
<h3>Polyhedra and Non-Polyhedra</h3>
|
|
<p>There are two main types of solids, "Polyhedra", and "Non-Polyhedra":</p>
|
|
<p><a href="polyhedron.html" class="larger">Polyhedra</a> <i>(they must have flat faces)</i>:</p>
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td style="text-align:center;"><a href="hexahedron.html"><img src="images/poly-cube.svg" alt="cube or hexahedron" height="88" width="88"></a> <a href="cuboids-rectangular-prisms.html"><img src="images/poly-square-prism.svg" alt="square prism" height="79" width="104"></a></td>
|
|
<td><a href="hexahedron.html">Cubes</a> and<br>
|
|
<a href="cuboids-rectangular-prisms.html">Cuboids</a> (<a href="../cuboid.html">Volume<br>
|
|
of a Cuboid</a>) </td>
|
|
</tr>
|
|
<tr>
|
|
<td style="text-align:center;"><a href="tetrahedron.html"><img src="images/poly-tetrahedron.svg" alt="tetrahedron" height="94" width="90"></a> <a href="hexahedron.html"><img src="images/poly-cube.svg" alt="cube or hexahedron" height="88" width="88"></a> <a href="octahedron.html"><img src="images/poly-octahedron.svg" alt="octahedron" height="86" width="85"></a> <a href="dodecahedron.html"><img src="images/poly-dodecahedron.svg" alt="dodecahedron" height="93" width="93"></a> <a href="icosahedron.html"><img src="images/poly-icosahedron.svg" alt="icosahedron" height="94" width="81"></a></td>
|
|
<td><a href="../platonic_solids.html">Platonic Solids</a></td>
|
|
</tr>
|
|
<tr>
|
|
<td style="text-align:center;"><a href="prisms.html"><img src="images/poly-tri-prism.svg" alt="triangular prism" height="70" width="105"></a> <a href="prisms.html"><img src="images/poly-square-prism.svg" alt="square prism" height="79" width="104"></a> <a href="prisms.html"><img src="images/poly-pent-prism.svg" alt="pentagonal prism" height="73" width="113"></a></td>
|
|
<td><a href="prisms.html">Prisms</a></td>
|
|
</tr>
|
|
<tr>
|
|
<td style="text-align:center;"><a href="triangular-pyramid.html"><img src="images/poly-tri-pyr.svg" alt="triangular pyramid" height="94" width="100"></a> <a href="square-pyramid.html"><img src="images/poly-square-pyr.svg" alt="square pyramid" height="78" width="115"></a> <a href="pentagonal-pyramid.html"><img src="images/poly-pent-pyr.svg" alt="pentagonal pyramid" height="94" width="90"></a></td>
|
|
<td><a href="pyramids.html">Pyramids</a></td>
|
|
</tr>
|
|
</tbody></table>
|
|
<p><span class="larger">Non-Polyhedra</span> <i>(when any surface
|
|
is not flat)</i>:</p>
|
|
|
|
<table style="border: 0; margin:auto;">
|
|
<tbody>
|
|
<tr>
|
|
<td style="text-align:center; background-color: white;"><a href="sphere.html"><img src="images/50px-sphere.jpg" alt="sphere" height="50" width="57"></a></td>
|
|
<td><a href="sphere.html">Sphere</a></td>
|
|
<td style="width:20px;"> </td>
|
|
<td style="text-align:center; background-color: white;"><a href="torus.html"><img src="images/50px-torus.jpg" alt="torus" height="50" width="68"></a></td>
|
|
<td><a href="torus.html">Torus</a></td>
|
|
</tr>
|
|
<tr>
|
|
<td style="text-align:center; background-color: white;"><a href="cylinder.html"><img src="images/50px-cylinder.jpg" alt="cylinder" height="50" width="47"></a></td>
|
|
<td><a href="cylinder.html">Cylinder</a></td>
|
|
<td> </td>
|
|
<td style="text-align:center; background-color: white;"><a href="cone.html"><img src="images/50px-cone.jpg" alt="cone" height="50" width="39"></a></td>
|
|
<td><a href="cone.html">Cone</a></td>
|
|
</tr>
|
|
</tbody></table>
|
|
<p> </p>
|
|
<ul class="large">
|
|
<li><a href="polyhedron-models.html">Polyhedron Models</a></li>
|
|
<li><a href="sphere-volume-area.html">Volume and Area of a Sphere Calculator</a></li>
|
|
<li><a href="spheroid.html">Spheroid</a></li>
|
|
<li><a href="cross-sections.html">Cross Sections</a></li>
|
|
<li><a href="vertices-faces-edges.html">Vertices, Faces, and Edges</a></li>
|
|
<li><a href="cone-sphere-cylinder.html">Cone vs Sphere vs Cylinder</a></li>
|
|
<li><a href="pyramid-vs-cone.html">Pyramid vs Cone</a></li>
|
|
<li><a href="prism-vs-cylinder.html">Prism vs Cylinder</a></li>
|
|
<li><a href="pyramid-vs-cube.html">Pyramid vs Cube</a></li>
|
|
<li><a href="cylinder-horizontal-volume.html">Volume of Horizontal Cylinder</a></li>
|
|
<li><a href="eulers-formula.html">Euler's Theorem</a></li>
|
|
<li><a href="pythagoras-3d.html">Pythagoras in 3D</a></li>
|
|
<li><a href="hypercubes.html">Hypercubes</a></li>
|
|
<li><a href="../builders-math.html">Builder's Math</a></li>
|
|
<li><a href="area-moments.html">Moments of Area</a></li>
|
|
</ul>
|
|
<p> </p>
|
|
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