Geometry Properties of a Rhombus
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A Smushed Square
Properties of a Rhombus

 
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 If you took a steel box and jumped up and down on it,

 it might get to looking like this:
 
 
 All of the sides would still be the same length,
 but the angles wouldn't be 90 degrees any more.
 We might have this:
 
 
 In math, we call this shape a RHOMBUS.
 (WOW! I wonder what planet they found that name on?)
 
 Anyway, a rhombus is still like a square in some ways
   1) All of the sides are still the same length.
   2) Sides across from each other are still parallel.
 
 But in one very important way,
 a rhombus is very different from a square.
   1) None of the angles are 90 degrees.
 
 The sides of the rhombus that are across from each other are parallel.
 That means we can play the old 
 "Two parallel lines and a line that crosses them"
 game here too!
 
 Back in the line game stuff, we had a rule that said
 that if two parallel lines were crossed by another line,
 the same side interior angles 
 would add up to 180 degrees,
 
 When we have a rhombus, that bit of info really helps.
 It tells us that ANY two angles that are next to each other
 will add up to 180 degrees.
 Can you see why?
 
 Just roll the rhombus over onto the next side
 and play the line game again.
 
 
 Example:
 Figure out the measure of the angles in this rhombus ...
 
 
 OK, in a rhombus two angles that are next to each other
 add up to 180 degrees.
 So that means we have:
 
 
 Now just play the game with each of these angles 
 and the unknown angle next to it ...
 We get:
 
 To figure out the area of a rhombus
 we need to know one more thing.
 We need to know how far it is
 from the top of the rhombus to the bottom.
 
 
 Here's why ...
 If we had a big knife, we could chop a corner off of the rhombus
 like this:
 
 
 And move the piece over like this:
 
 
 Now we have a rectangle,
 and rectangles are easy to deal with ...
 
 Example:
 Find the area of this rhombus:
 
 
 Chop it up and reassemble it ...
 
 
 Multiply the length times the width
 to get the area ...
 
 One other thing you should know about a rhombus.
 A rhombus has less area than a square 
 that has sides of the same length.
 (Hey, if you squash something it will hold less stuff)
 
 
 The diagonal lines in a rhombus work sort of like they do in a square:
   1) They chop the corner angles exactly in half
   2) They chop each other exactly in half
   3) The angles we get where they cross are exactly 90 degrees
 
 They are different from the diagonal lines in squares in one big way:
   1) Rhombus diagonals are NOT the same length as each other.
 
 

   copyright 2008 Bruce Kirkpatrick

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