In this part, you will take stock of what you have learned about reflections.
Learning Objectives
Students will
Put together and review all they have learned about reflections
Materials
Computer and Internet connection
Instructional Plan
Taking Stock...Reflections
1. What is necessary to describe a reflection?
2. Draw a shape, a mirror line, and the image of the shape reflected across
the mirror line.
3. Draw a shape with a center of rotation that has the property that the shape looks exactly the same after rotation through 120°. What kind of symmetry
does your shape have?
4. Draw shapes with (a) bilateral symmetry, (b) 3-fold dihedral symmetry, and
(c) 4-fold dihedral symmetry.
5. If you see a symmetric design, how do you determine whether the design has rotational or dihedral symmetry?
6. If you see a design with dihedral symmetry, how do you determine where the mirror lines are?
7. Summarize what happens when a shape is reflected twice.
Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
Use various representations to help understand the effects of simple transformations and their compositions.
Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.
References
For All Practical Purposes: Introduction to Contemporary Mathematics,
W.H. Freeman and Company, New York, 1997
Understanding Congruence, Similarity, and Symmetry Using Transformations and
Interactive Figures: Visualizing Transformations, NCTM Principles and Standards
for School Mathematics: E-example 6.4. http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm
The National Council of Teachers
of Mathematics is a public voice of mathematics education, providing
vision, leadership, and professional development to support teachers
in ensuring mathematics learning of the highest quality for all
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should not be interpreted as official positions of the Council.
