Objectives
To find compositions of reflections, including glide reflections
To classify isometries
In the Solve It, you looked for a way to use two reflections to produce the same image as a given horizontal translation. In this lesson you will see that any isometry can be expressed as a composition of reflections.
Essential Understanding If two figures in a plane are congruent, you can map one onto the other using a composition of reflections.
The theorems in this lesson lead to the fact stated above. Complete proofs of these theorems are beyond the scope of this course, but Problems 1 and 2 suggest approaches to the proofs of Theorems 9-1 and 9-2. Theorem 9-2 is the converse of Theorem 9-1.
A translation or rotation is a composition of two reflections.