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If you draw two lines in a plane so they never cross, then we call them parallel lines. Let's
take a close look at these two parallel lines. Let's call the top line L1 and the bottom
line L2. There's a symbol you use to indicate these two lines are parallel. Double vertical
lines! Notice this symbol looks like two parallel lines. Coincidence? I don't think so. You
would read this aloud as "L1 is parallel to L2."
Suppose you draw a line that crosses the parallel lines. We call this double crosser a transversal.
The point where the transversal crosses L1 makes 4 angles. And the point where the transversal
crosses L2 makes 4 angles. An interesting and useful fact is that corresponding angles
are equal to one another! These angles are equal. These two are equal to each other.
These angles are the same. and these are identical, too!
And let's not forget that whenever two lines cross, opposite angles are equal. Another
name for opposite angles is "vertical angles."
So these angles are equal. and these vertical angles are equal, too! This means that when
a transversal crosses two parallel lines, this angle equals this corresponding angle...
And since vertical angles are equal, this angle is equal to this angle... And this angle
is equal to this angle! So in this picture there are 8 angles, and four of them are equal!
Wait, it gets better. Look at the remaining four angles. This angle is equal to this corresponding
angle. which equals this vertical angle. which equals this corresponding angle. So the remaining
four angles are also equal!