Congruences between a square and itself

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SUMMARY

The discussion focuses on the congruences of a square, specifically identifying that all four sides (A, B, C, D) and four right angles (e, f, g, h) are congruent to each other. Each side is congruent to every other side, and similarly, each angle is congruent to the others. The square itself is congruent to itself, affirming the concept of reflexive congruence. The discussion also touches on the labeling of a square's vertices and the permutations that maintain the square's identity.

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  • Basic knowledge of vertex labeling in geometry
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Homework Statement



What are the congruences between a square and itself?

Homework Equations



none

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...
 
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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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