Special Pair of Lines in the Coordinate Plane

In the applet below, feel free to move ANY LARGE POINT anywhere you'd like AT ANY TIME. Interact with this applet for a few minutes. Be sure to tamper with all sliders and be sure to move the LARGE POINTS around. After doing so, please reflect on these dynamics by answering the few questions that follow.

1.

Press the reset button. Slide the long black slider slowly (once again) and stop it at the exact moment the 2nd pink angle reaches the 2nd line. What does the action of the pink angles imply about both black lines? How/why do you know this to be true?

2.

Now resume sliding the slider where you left off in question (2) above. What does the motion of the 2nd right triangle imply about both black lines?

3.

What causes the right triangle (that appears) to turn blue? What causes it to turn red? Please describe as best as you can.

4.

Write a conditional (a statement of the form "If _____, then _____") that describes the phenomena through which you've just dynamically interacted.

5.

If we formed the converse ("flip") of the conditional ("If _____, then _____") statement you wrote for (4), would that statement always be true? That is, if you swap both hypothesis and conclusion of the statement you wrote for (4), would this statement be true? Why? Why not? Explain.

Quick (Silent) Demo