Chapter 4.7, Problem 36HP

To determine

To explain:

If a glide reflection a congruence transformation or not.

Answer to Problem 36HP

Yes, a glide reflection is acongruence transformation.

Explanation of Solution

Given information:

  

A glide reflection is a reflection over a line and then a translation in a direction that is parallel to theline of reflection.

In a congruence transformation, the preimage and image are congruent.

Yes, a glide reflection is acongruence transformation.

In the diagram,

  $\begin{array}{l}AB=DE\\ BC=EF\\ AC=DF\end{array}$

So,

  $\begin{array}{l}\overline{AB}\cong \overline{DE}\\ \overline{BC}\cong \overline{EF}\\ \overline{AC}\cong \overline{DF}\end{array}$

Thus, $\Delta ABC\cong \Delta DEF$ .