# Parallel Lines Congruent Segments Theorem

- Author:
- Tim Brzezinski

- Topic:
- Congruence, Straight Lines

Interact with the following applet for a few minutes. Be sure to change the location of each BIG point. Be sure to move the slider at some point as well. Then complete the activity that follows.

The applet above suggests a very powerful, yet often unused theorem in all of geometry. See if you can rearrange the list of words below to form a conditional ("If-then") statement that states what is shown in the applet above!
segments one parallel then
every cut transversal segments lines
or congruent they transversal cut
If congruent off on more
3 on off

Write a formal proof of the conditional statement (whose words you've arranged) above.