More Symmetry
In this lesson, we continue our exploration of shape and symmetry, using mirrors to reflect shapes and represent lines of symmetry. For example, where would you place a mirror on an isoceles right triangle in order to reflect a square?
If you actually try this with a mirror, you will see that a variety of shapes result from reflecting various parts of the triangle in the mirror. However, only certain positions will result in a square. How would you describe all the positions of the mirror that produce a square?
What are the common elements in every position that produces a square? Students usually notice two things...
What about a triangle? How would you place the mirror to reflect one? How would you describe the positions of the mirror? What attributes does the triangle have? Click here here to see.
This exploration of symmetry with mirrors and shapes leads students to many observations about the relationships between various two-dimensional shapes. Using mirrors, students try to reflect certain shapes from a variety of other shapes. Using the diagrams below, can the following shapes be reflected? If not, why not? What other observations can you make? Give them a try!
A solid understanding of symmetry and congruence are fundamental to further study in geometry, both two-dimensional and three-dimensional. Through explorations like these, students begin to develop many intuitions and concepts relating to these important ideas which will be built on in later geometry lessons.
