Geometry Heavy Duty Triangle Definitions
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Triangle Deffs
Heavy Duty Triangle Definitions

 

 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

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