[b]The 2 lines shown below are PARALLEL LINES drawn within the coordinate plane. [/b][br]Interact with this applet for a few minutes. (Be sure to adjust the sliders.) [br]Feel free to move the BIG WHITE POINTS anywhere you'd like as well. [br][br]Then, answer the questions that follow.
What is the measure of the gray angle? How do you know this?
The gray angle measures 90 degrees (or [math]\frac{\pi}{2}[/math] radians.) [br]If two lines cross to form congruent, adjacent angles, then those lines must be perpendicular. [br]Hence, the gray angle measures 90 degrees.
What can you conclude about any 2 non-vertical parallel lines drawn within the coordinate plane?
[b]If two non-vertical lines drawn in the coordinate plane are parallel, then their slopes are equal! [/b][br][br]The slope triangle from the first line was simply translated-by-vector to lie along the 2nd line. [br]This implies that the two parallel lines have equal slopes!