



Math
detective school now moves on to triangles.






What
makes a triangle a triangle? 





Three
line segments that join together 


end to
end to end. 


Like
this: 











Not this: 











No matter
what the triangle looks like, 


the
angles on the inside always, always, always, 


add up to
180 degrees. 





Here are
a few other triangle definitions 





Right
Triangle 


Any
triangle that has a 90 degree angle in it. 





Acute
Triangle 


Any
triangle where all of the angles are less than 90 degrees, 


or any
triangle that all other triangles think look nice. 





Obtuse
Triangle 


Any
triangle that has an angle greater than 90 degrees 





VERY
OBTUSE TRIANGLE POP QUIZ: 


Can a
triangle have more than one angle 


greater
than 90 degrees? 





Isosceles
Triangle 


Any
triangle where two sides (or angles) 


are the
same size (congruent). 





Equilateral
Triangle 


Any
triangle where all three sides (or angles) 


are the
same size (congruent). 





These
next definitions have to do 


with
comparing one triangle to another triangle. 





Corresponding
Angles 


Comparing
the measure of an angle in one triangle 


to an
angle in another triangle. 


Generally,
when we talk about corresponding angles 


we rotate
the triangles so that the angles we want to compare 


are in
the same place in each triangle. 





Example: 


Make
angles A and W corresponding angles ... 











We didn't
really have to rotate the triangle. 


We could
just compare the angles A and W in our mind. 


But
rotating the triangle makes comparing easier. 





Corresponding
Sides 


Comparing
the measure of a side of one triangle 


to a side
of another triangle. 


Just like
before, we can just compare them in our mind, 


or rotate
the triangle so that they are in the same place 


on each
triangle. 





Congruent
Triangles 


Any two
triangles that have the same size angles 


and the
same length sides 





Example: 











These are
all congruent to each other 





If you
look close, you will see that the second triangle 


can be
rotated to look just like the first one. 


But if we
rotate the third one, 


all we
can do is make a mirror image. 











That's
Okay. In our minds we can compare the sides ... 











and the
angles. 











So great. 


If for
each angle in one triangle 


there is
an angle of the same size in another triangle, 


and if
for each side in one triangle 


there is
a side of the same size in the other triangle, 


then the
triangles are congruent. 





But hey!
They never give us that much information 


in these
problems. 





They only
give us bits and pieces. 





I wonder
just how much we need to know 


to say
that two triangles are congruent? 


(Ya
probably knew that was coming, eh?) 





copyright 2005 Bruce Kirkpatrick 
