



Now
let's put this line stuff together.



Take two
parallel lines ... 











add a
line that crosses the two ... 











and some
special things happen. 





The cross
on the top 











makes the
same angles as the cross on the bottom. 











There's a
lot of math shenanigans that show why this is so. 


You
really don't need any of that stuff right now. 


You can
probably see that when you have two lines that cross ... 











moving
the horizontal line up and down 


doesn't
change the size of any of the angles ... 











So one
line that is moved up, 


or two
parallel lines are 


REALLY
THE SAME THING! 











That
means angles 1 and 3 AND 


5 and 7
are all the same size! 





For that
same reason we can say that angles 


2 and 4
AND 6 and 8 are all the same size. 





Here's
how problems you might get with this work. 





Example: 


Say you
have two parallel lines and a line that crosses them. 


Say the
angles are labeled with letters from A to H. 


They tell
you that the measure of angle A is 119 degrees 


and ask
you to find the measure of the other angles. 











F = H = D
= 119 degrees 

















More
Examples: 


Another
trick that you might have noticed is that 


any two
angles that are next to each other 


add up to
180 degrees 











Or an
even trickier thing is that 


two
angles on the same side of the crossing line 


closest
to each other add up to 180 degrees 











and that
two angles on the same side of the crossing line 


farthest
from each other add up to 180 degrees too! 











In fact,
we can pick any two angles. 


They will
either be equal to each other 


or add up
to 180 degrees. 





As you
can see, all of this is no big deal. 


But we
know that math people LOVE to think up names for stuff. 


So they
took this one little trick 


and
thought up about a zillion names for it. 





copyright 2005 Bruce Kirkpatrick 
