Geometry Properties of Rectangles
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A Stretched Square
Properties of Rectangles

 

 Take a square and stretch it in one direction.

 

 

 
 You get a rectangle.
 
 The angles are still 90 degrees.
 Sides across from each other are still the same size.
 Sides across from each other are still parallel.
 
 We could use a bunch of the games from back in
 "two lines crossed by another line"
 to show that the sides across from each other 
 are really parallel.
 

 

 
 Back then, we had a rule that said
 "If two lines are crossed by another line,
 and the same side interior angles add up to 180 degrees
 then the lines are parallel"
 
 So when you have a rectangle,
 the sides across from each other really are parallel.
 
 Wonderful.
 
 Diagonal lines inside a rectangle don't work exactly the same way
 as they do in a square.
 Some things do work the same way,
 some things don't.
 

 

 
 THINGS THAT DO WORK THE SAME WAY:
   1) The two diagonal lines are both the same length
   2) The two diagonal lines cur each other exactly in half
   3) Each diagonal line creates right triangles with two of the rectangle sides
 
 THINGS THAT DON'T WORK THE SAME WAY
   1)The angles we get where the diagonal lines cross are NOT 90 degrees
   2) The diagonal lines DO NOT cut the angles 
      at the corners of the rectangles exactly in half.
 

   copyright 2005 Bruce Kirkpatrick

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