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