Geometry Properties of Squares
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What a Square
Properties of Squares

 

 A square has four sides that are all the same length.

 Like this:
 

 

 
 Another special thing about a square
 is that all of the angles are the same size.
 They all measure 90 degrees.
 

 

 
 If something has four sides 
 and they are all the same length
 and four angles inside
 and they are all 90 degrees.
 IT'S A SQUARE
 
 One other thing about a square,
 is that the sides across from each other
 are all parallel.
 
 To find the area of a square, 
 just multiply the length times the width.
 
 This is pretty easy to do with squares
 because the length and width are the same number.
 

 

 
 If you draw a line from the top left corner of a square
 to the bottom right corner of the square ...
 

 

 
 You get a line called a diagonal.
 (It goes diagonally across the square.)
 So for once, one of these fancy math names names sense!
 
 This line cuts the 90 degree angles 
 at the corners of the square exactly in half.
 

 

 
 This diagonal is also part of a right triangle
 that is hidden in the drawing.
 

 

 
 That means, 
 if we know how long the sides of the square are ...
 we can figure out the length of the diagonal!
 

 

 
 There is nothing special about the two corners
 we used to make the diagonal lines.
 We could also use the other two corners
 to draw the diagonal line.
 

 

 
 This one also cuts the corners exactly in half.
 

 

 
 And makes some right triangles inside the square.
 

 

 
 The sides of the square are the same size 
 as they were a moment ago.
 That means that this diagonal line will work out to be
 the same length as the other one was.
 

 

 
 Where the two diagonal lines cross in a square,
 two special things happen.
 1) They both cut each other exactly in half
 2) All the angles at the cross are 90 degrees
 That means we now have four right triangles
  hidden in the square.
 

 

 
 These little right triangles are all the same size as each other.
 

 

 
 If we know how long the sides of the square are,
 we can figure out the length of the sides of these little triangles.
 
 Example:
 Figure out the length of the short triangle sides
 when the length of each of the sides of the square is 5.
 
 The short triangle sides are the same size as each other.
 Call each one X.
 

 

 
 Some people, OK mostly math people, 
 don't like to see roots on the bottom of a fraction (the denominator).
 
 We can get the root out of there
 by multiplying the answer by a special name for 1.
 This name:
 

 

 
 So we get:
 

 

 
 Math people just love that last step (don't ask me why).
 

   copyright 2005 Bruce Kirkpatrick

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