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Congruences between a square and itself

  1. Oct 28, 2008 #1
    1. The problem statement, all variables and given/known data

    What are the congruences between a square and itself?


    2. Relevant equations

    none

    3. The attempt at a solution

    Let A, B, C, and D be the sides of the square and e, f, g and h the four right angles.

    All four sides are congruent to themselves--same with the angles.

    Side A is congruent to Side B
    Side A is congruent to side C
    Side A is congruent to side D
    Side B is congruent to side C
    Side B is congruent to side D
    Side C is congruent to side D

    And we can symmetrically list the congruences between the angles.

    And the whole square is congruent to itself...

    It's a simple problem but there's no answer key in the text and I'm wondering if I'm right to count all the reflexive congruences...
     
  2. jcsd
  3. Oct 29, 2008 #2

    HallsofIvy

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    Saying "side A is congruent to side B" does not say the square is conguent to itself.

    Since you can "label" a square by listing its vertices in order, ABCD, how many different ways of ordering ABCD give the same square? BCDA does but BACD does not. Do you see why?
     
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