Reflections over Intersecting Lines

Bob Allen
We've explored reflections, rotations, and translations. Now we're going to go a bit more basic and work only with reflections. You will be exploring what happens to a figure when reflected over two parallel lines. 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.


1. Measure BED in that order. If you get an angle measure larger than 180, undo and try again. 2. Using the Reflect about Line tool, reflect the flag over line f. 3. Using the Reflect about Line tool, reflect the flag prime over line g. 4. Measure JEJ''.

Collecting Data

2. Record the original measure of BED and JEJ" as Trial 1. Then move any or all of the following objects: points D or B, or the flag. Record the new angle measures, BED and JEJ'', label them 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.


Compare the two angle measures in your table. What do you notice? Write a conjecture about the those two values. Here's a start: If a figure is reflected over two intersecting lines, then...

What does this look like?

Look at the preimage flag and the second image (double prime). Does this look like a translation, rotation, reflection, or something new? What else do you notice? How does it move? Are any other points important? (Yes, this is a little open ended.)

Press the Turn In button ONCE and then wait patiently for a few moments. If nothing seems to happen, or if you do not have a Turn In button, call for me. If you have homework to complete, do that while everyone finishes.