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Motions in Geometry

Section 11.1 Congruence and Constructions: Defines congruence in terms of mappings and introduces constructions to establish the triangle inequality and common congruence properties of triangles. Subsections: Mappings; Constructing Segments and Angles; Constructing Triangles; Constructing Bisectors; Constructing Perpendicular and Parallel Lines; Circumscribing Circles about Triangles; Constructions with a Mira; Problem-Solving Application One-page Math Activity: Tracing Figures from Motions with Tile

Section 11.2 Congruence Mappings: Illustrates the congruence mappings of translation, reflection, and rotation with physical examples of 2-D and 3-D figures, and outlines methods for creating Escher-type tessellations. Subsections: Translations; Reflections; Rotations; Composition of Mappings; Congruence; Mapping Figures onto Themselves; Escher-Type Tessellations; Problem-Solving Application One-page Math Activity: Rotating, Reflecting, and Translating Figures on Grids

Section 11.3 Similarity Mappings: Illustrates similarity mappings with both positive and negative scale factors for 2-D and 3-D figures, and develops the familiar similarity properties of triangles. Subsections: Similarity and Scale Factors; Similar Polygons; Similar Triangles; Problem-Solving Application; Scale Factors with Area and Volume; Sizes and Shapes of Living Things One-page Math Activity: Enlargements with Pattern Blocks
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg:: ::/sites/dl/free/0073022845/97052/tessalation.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (8.0K)</a> <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg:: ::/sites/dl/free/0073022845/97052/tessalatinshot.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (9.0K)</a>
If you have ever formed an Escher-type tessellation by tracing figures on paper or at a window, you will be amazed at the power of this interactive. You will be pleasantly surprised at how quickly figures and tessellations can be created.
Click Here to Launch the Applet



In This Chapter

Motions in Geometry
Internet Resources
Math Applet

11.1 Congruence and Constructions
Bibliography

11.2 Congruence Mappings
Bibliography

11.3 Similarity Mappings
Bibliography








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