Site MapHelpFeedback9.4 Symmetric Figures
9.4 Symmetric Figures


Explains reflection and rotation symmetries for plane and space figures and illustrates these symmetries with examples from architecture and nature.

Subsections: Reflection Symmetry for Plane figures; Rotation Symmetry for Plane Figures; Reflection Symmetry for Space Figures; Rotation Symmetry for Space Figures; Problem-Solving Application

One-page Math Activity: Symmetries of Pattern Block Figures


The Investigation poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.

Click on the Read Me file below to open the investigation in a Word file:

Read Me - Mirror Cards Instructions (Word Format) (36.0K)


Laboratory Investigation 9.4

Mirror Cards Mirror Cards were developed to teach spatial relationships and symmetry informally in early grades.* The idea is to place a mirror on some initial card, such as the one in the following figure, to obtain a pattern which is on another card.

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Starting Points for Investigations

  1. Using sketches of the initial card above draw a line on each sketch to represent the placement of a mirror to show how each pattern on the following cards can be obtained.

    2. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073022845/78543/LI_9_4b.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"> (21.0K)</a>

  2. Sketch some other figures that can be obtained from the initial card given above and show a line representing the mirror which produces each figure.

  3. Design an initial card and show some figures that can be obtained from it. For each figure you obtain, draw a line on your initial card to represent the placement of the mirror.

*M. Walter, "An Example of Informal Geometry: Mirror Cards," Arithmetic Teacher 13 (October 1966): 338-352.








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