# Congruences between a square and itself

1. Oct 28, 2008

### Pascal's Pal

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. Oct 29, 2008

### HallsofIvy

Staff Emeritus
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?