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information in the relevant cells of the table for<br />
Problem 4.<br />
Although the list of quadrilaterals may appear to<br />
be ordered in some sort of mathematical scheme,<br />
actually it is in reverse alphabetical order.<br />
Answers<br />
1. Answers will vary.<br />
2. Answers will vary.<br />
3. Answers will vary.<br />
4. See table below.<br />
Discussion Answers<br />
A. Yes. A figure with n lines of symmetry<br />
has n-fold rotation symmetry.<br />
B. There are figures with three- and fourfold<br />
rotation symmetry, but no lines of<br />
symmetry; however, they are not triangles<br />
or quadrilaterals. Figures with exactly one<br />
line of symmetry cannot have rotation<br />
symmetry. Figures with exactly two, three,<br />
and four lines of symmetry must have<br />
two-, three-, and four-fold rotation<br />
symmetry, respectively.<br />
C. Answers will vary.The scalene triangles<br />
have no symmetries.The isosceles figures<br />
have exactly one line of symmetry. If you<br />
join the midpoints of a rhombus, you get a<br />
rectangle, and vice versa.<br />
D. The two lines of symmetry of the rhombus<br />
or rectangle are among the four lines of<br />
symmetry of the square.A square is a<br />
rhombus, but a rhombus is not necessarily a<br />
square.The line of symmetry of an isosceles<br />
triangle is among the three lines of symmetry<br />
of the equilateral triangle.An equilateral<br />
triangle is isosceles, but an isosceles triangle is<br />
not necessarily equilateral.<br />
Lab 5.3: One Mirror<br />
Prerequisites: Students should be familiar with<br />
the names of the triangles and quadrilaterals<br />
listed in the chart. In this book, those names were<br />
introduced in Lab 1.5 (Angles in a Triangle) and<br />
Lab 5.2 (Triangle and Quadrilateral Symmetry).<br />
In this activity, always use the most generic<br />
version of a figure: isosceles means a triangle<br />
with exactly two equal sides, rectangle means<br />
a rectangle that is not a square, and so on.<br />
If you have never used mirrors with your class,<br />
you should consider giving students a little time<br />
to just play freely with them at the start of the<br />
lesson.Then, you may discuss the following<br />
examples as an introduction.<br />
Rotation Symmetry<br />
Line Symmetry None Two-fold Three-fold Four-fold<br />
No lines<br />
One line<br />
Two lines<br />
AS, RS, OS,<br />
HE, GT, GQ<br />
AI, RI, OI,<br />
KI, IT<br />
PA<br />
RH, RE<br />
Three lines<br />
EQ<br />
Four lines<br />
SQ<br />
Geometry Labs Notes and Answers 193<br />
© 1999 Henri Picciotto, www.MathEducationPage.org
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