



Well
the last page was kind of interesting,



but what
did it have to do with math? 





We prove
stuff in math the same way 


as those
detectives work. 





We have
our bag of definitions, theorems and postulates. 





We show
up at the crime scene (the problems). 





We use
our tools and the information given at the scene 


to solve
the problem. 





You have
already worked with most of these ideas, 


we just
didn't get real fancy and call them 


theorems
and postulates back then. 





This time
they're all dressed up. 


It' s
math detective school. 





POINT 


Just a
place in space. So tiny that we could never see it. 


We just
know where it is. 





RAY 


A
straight line coming out of a point 


in some
direction. It goes forever ... 











LINE 


Like a
ray, but it goes forever in both directions. 











LINE
SEGMENT 


A piece
of the line. 











PLANE 


Like a
very flat sheet of paper. 


But the
plane has no edges. 


It goes
forever ... 











CONGRUENCE 


Say there
were two identical twins 


that were
so much alike that nobody could tell them apart. 


Everything
about them was the same, 


but they
aren't the same person. 


They are
CONGRUENT. 


So in
math, two line segments that are the same length 


or two
angles that are the same number of degrees 


or two
objects that are the same size and shape 


ARE
CONGRUENT. 





MIDPOINT
OF A SEGMENT 


If the
piece of a line segment on one side of a point 


is the
same length as the piece of the line segment 


on the
other side of the point, 


that
point is the midpoint of the segment 


(and the
two pieces are congruent). 











SEGMENT
BISECTOR 


This is
like the midpoint deal, 


but this
time we use another line segment (or ray or line) 


to cut
the segment into two equal pieces. 











ANGLE
BISECTOR 


A ray
that cuts an angle into 2 angles 


that are
equal to each other. 


For
example: 











SUPPLEMENTARY
ANGLES 


Any two
angles that add up to 180 degrees. 











COMPLEMENTARY
ANGLES 


Any two
angles that add up to 90 degrees 











ADJACENT
ANGLES 


Two
angles that share one side but don't overlap 











VERTICAL
ANGLES 


When 2
lines cross, the angles across from each other 


are
called VERTICAL ANGLES. 


They have
the same measure. 











PERPENDICULAR
LINES 


When two
lines cross, if all the angles at the cross are 90 degrees 


the lines
are PERPENDICULAR. 











We could
also turn this definition upside down and say this. 


If two
lines that cross are perpendicular 


all the
angles are 90 degrees. 





When we
can turn something like this upside down 


and say
something else, 


that
other thing we can say is called a COROLLARY. 





PERPENDICULAR
BISECTOR 


Hey, we
know what a bisector is. 


We just
had what perpendicular means. 


Just put
them together. 











If a line
(or segment or ray) cuts another segment 


into two
equal pieces and also makes 90 degree angles, 


it is the
PERPENDICULAR BISECTOR of the other segment. 





DISTANCE 


The
distance between two points 


is the
length of the line segment between them. 











PARALLEL 


Two lines
that are in the same plane 


that
never cross are parallel. 











Two line
segments or rays that are always 


the same
distance apart are PARALLEL. 











copyright 2005 Bruce Kirkpatrick 
