@ganeshie8
How can I write a definition of a square in terms of points, lines, parallel, perpendicular and congruence?
Please, help
I don't want to describe it.

- Loser66

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- chestercat

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- Loser66

I have "incidence" also.

- anonymous

Haha! I don't want to either. But that's not a good reason to ask others to do it for you.

- Loser66

@ospreytriple If I don't know how to, I am a right to ask. A bunch of definition on internet, right?

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## More answers

- Loser66

and I am not as good as you to know everything. :)

- anonymous

Sorry if I offended you @Loser66 . I was commenting on your statement "I don't want to describe it."

- Loser66

Yes, you did offend me. hehehe... but I am cool because you point out how stupid I am and it is true.

- anonymous

You know what a square is. I would start b y writing something out in plain English and then working the mathematical terminology into it.

- Loser66

A pair of parallel lines perpendicular to another pair of parallel lines at 4 points with equidistant sides forms a geometry called a square.
right?

- Loser66

hahaha.... my bad English!!

- ganeshie8

teamviewer?

- Loser66

again? yes.

- BloomLocke367

I already helped you with this question..

- Loser66

@BloomLocke367 I appreciate what you did but I didn't satisfy with it.

- ganeshie8

|x| = a and |y| = a
does that work

- ganeshie8

if not, may i know what exactly are you looking for

- Loser66

if you say |x|, then I must define the | | term.

- Loser66

We have "congruence" is undefined term on our definition.

- ganeshie8

go ahead define them
shouldnt be hard

- Loser66

so, before giving out the definition of a square, I must add the definition of | | term, rightg?

- Loser66

if so, why not a quadrilateral or a rhombus? It is quite easier, right?

- anonymous

How about defining the four vertices as \((x_1, y_1), (x_2, y_2), (x_3, y_3), x_4, y_4)\) such that \(x_1=x_3\), \(x_2=x_4\), \(y_1=y_2\), and \(y_3=y_4\). Then you have to add the appropriate line segment connecting the correct vertices. That do it?

- ganeshie8

let me just tag @Concentrationalizing

- Loser66

Thanks

- Loser66

|dw:1441560226473:dw|

- anonymous

Hate to be a nitpicker, but the sides of a square are line segments, not lines.|dw:1441560429401:dw|Is line segment not permissible in the definition?

- Loser66

I did for a circle, it is a set of points whose equidistant from a fixed point

- anonymous

You might want to constrain your circle definition to a 2-dimensional figure. Otherwise, you'll end up with a sphere.

- Loser66

|dw:1441560688148:dw|

- Loser66

ok, thanks for the tip. I will add 2D and 3D in

- Loser66

Think of my definition of a square? I am not a native American so that It is hard for me to jot down the definition of something. hehehe....

- triciaal

@Loser66 do you have enough now or do you still need more?

- Loser66

Surely I need as much as possible.

- triciaal

what I had before
a square is a set of 4 points such that when they are connected by lines creates 2 sets of parallel lines that are perpendicular to each other and all 4 segments are the same lengths.

- Loser66

Thank you so much.

- anonymous

Couple of issues I can see:|dw:1441562290366:dw|Four points connected by line segments? Also, is a square really a set of four points? Or is it a set of four line segments?

- triciaal

4 points when connected by lines is that what you disagree with ?

- anonymous

Yes. Which points are connected to which other points?

- triciaal

a square is the shape of the figure produced when ....

- anonymous

You might consider beginning with " a 2D geometric figure consisting of four congruent line segments..."

- triciaal

the segments you get after you have the points and connect them

- Loser66

@ospreytriple Yes, I did. I constrain them in 2 D, so that the parallel lines are in the same plane and they don't turn to the skew lines in 3D

- triciaal

very good to include it is a 2D figure produced when.....

- triciaal

is @ospreytriple the only one who did not see a square from my description?

- anonymous

"...arranged such that each endpoint is connected to exactly one other endpoint and each line segment is perpendicular to the two line segments to which it is connected." What do you think?

- Loser66

@triciaal I don't think so, he is just figure out how a reader can critique your definition. That is the way we project a geometry.

- Loser66

oh, my bad, I got you

- Loser66

I have to go now. If you guys have another guidance. please, let it here. I will pick it later.
Thanks in advance.

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