# Reflections over Parallel Lines: Distances

- Author:
- Bob Allen

**REMEMBER**: Mistakes are a good thing. No one, and I mean no one, gets every construction right on the first try. This isn't brain surgery. Nothing will crash if you make a mistake. And starting over is sometimes the best way to go. So there's the do over symbol in the upper right hand corner.

## Instructions for the first set of reflections.

*DE*. 2. Measure the distance from point

*D*to any part of line

*f*that's not a point. You might have to use the Move tool to move the two measurements off of one another. 3. Using the

**Reflect about Line**tool, reflect

*ABC*over line

*f*. 4. Using the

**Reflect about Line**tool, reflect

*A'B'C'*over line

*g*.

## Distance from a point to a line

1. Why are the two distances, *DE* and *Df*, the same? (And if they're not the same, you have done something incorrect. Go back and try again. Remember, nothing has exploded. Not even your grade.) Hint: What distance are we measuring from a point to a line?

## Collecting Data

2. Measure the distance from A to A''. Record the distance between the lines (either *DE* or *Df*) and AA'' in the box below and call it 'Trial 1."
Then move any or all of the following objects: the pink dots on line *f*, point *D*, or *ABC*. Record the distance between the lines and AA'' and label it Trial 2 in the box below.
Repeat the previous step three more times, labelling new steps as Trials 3 through 5 respectively.
Your data should look something like this:
Trial 1 ### ###
Trial 2 ### ###
and so on.

## Conjecturing

Compare the two distances recorded in the five trials above. State a conjecture about the two distances. Here's a start... If a figure is reflected over two parallel lines, then...