Composition of Reflections

 This exercise will teach what happens to a figure when it is reflected across two different intersecting mirror lines

Instruct students to work through the above exercise.  Ask them to describe in their own words, based on their experience, a composition of two reflections across two different intersecting mirrors.  In addition, a relationship between the angle formed by the mirrors and the rotation angle should be established.  Answers should be compared and discussed in class.  This discussion will provide an opportunity for the teacher to do the following demonstration.

Obtain two 12 in. x 12 in. mirrors that are hinged in the middle.

Place a piece of making tape with a classmates name spelled out in a corner of one of the mirrors.

As the name is reflected in the other mirror it appears to be written backwards.

As the reflection of the backwards name is reflected in the mirror with the masking tape, the name is no longer backwards.  (a real example of a composition of two reflections)

The conclusion of this discussion should end with the establishment of a working description of this geometric concept.

A composition of two reflections across two different mirror lines is a rotation and the resulting angle is twice the angle between the two reflection axes.