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Mathematics 19 Online
OpenStudy (aric200):

Which MUST be a square?

OpenStudy (anonymous):

This isn't another one of your super-tedious algebra problems is it? :>

OpenStudy (aric200):

OpenStudy (aric200):

I believe they all look like squares :I

OpenStudy (aric200):

But which one most represent a square

OpenStudy (anonymous):

that's coz you need to see through tricks :>

OpenStudy (anonymous):

but C is true...as all thee diagonals are equal...

OpenStudy (anonymous):

right... so? lol

OpenStudy (anonymous):

anyway... what does a four-sided figure need to be, to be a square? ^^

OpenStudy (aric200):

I know all must have 4 Right angles

OpenStudy (anonymous):

it DOES have to have four right angles, don't it? ^^ but don't ALL rectangles also have four right angles? :>

OpenStudy (anonymous):

yupp..but there corners have some deviation from def of a square..!and also in D two sides equal are given but no idea about other two,in A on corner is out of square and in B each four corners are shared by some other .so C gives appreciable ans by def of square.

OpenStudy (aric200):

Yes I suppose all rectangles Do have 4 right angles

OpenStudy (anonymous):

and for any fig to be squre..its all sides must be equal...

OpenStudy (anonymous):

silly zaibali.... have you drawn a perfect rectangle recently? ^^

OpenStudy (anonymous):

|dw:1404403696280:dw| ok.... non-square rectangle... ^^

OpenStudy (aric200):

Why does this have to be so difficult haha

OpenStudy (anonymous):

|dw:1404403718394:dw| but I'll bet my hat that its diagonals bisect each other, just like in figure C ^^

OpenStudy (anonymous):

see the central angle of all the diagonal made with each other...in C all are at 45 degree...whats about here...???

OpenStudy (agent0smith):

Things that (individually) do NOT guarantee a quadrilateral is a square: Four right angles All sides are congruent Things that DO guarantee a quadrilateral is a square: diagonals are congruent

OpenStudy (anonymous):

But don't ALL rectangles have congruent diagonals? :/

OpenStudy (anonymous):

mister agent0smith... congruent diagonals must also be perpendicular for said four-sided-polygon to be a square, no? ^.^

OpenStudy (aric200):

Guys I am going to have to prove a rhombus to so :I

OpenStudy (anonymous):

well, you can bet YOUR hat that one of these figures is definitely a rhombus ^^

OpenStudy (aric200):

Its a different question haha

OpenStudy (anonymous):

well finish this one first >:( which is your square? ^^

OpenStudy (aric200):

Um well could it be A?

OpenStudy (aric200):

Knowing that all sides are shown to be equal and knowing one angle is right that must mean that the rest of the angles must also be right angles?

OpenStudy (anonymous):

It could... but IS it? ;) confidence, lol ^^

OpenStudy (anonymous):

all sides are congruent means it's a rhombus... but how do you know it's a square? :)

OpenStudy (anonymous):

oh you already answered that... lol ok never mind good job :P

OpenStudy (aric200):

Because I see the shape :(

OpenStudy (agent0smith):

Yeah I think only A is actually.

OpenStudy (anonymous):

@agent0smith awsum :> @aric200 that should never EVER be your reason....

OpenStudy (agent0smith):

I messed up earlier, good point peterpan. I was instinctively assuming "if they're perpendicular" but didn't write it.

OpenStudy (aric200):

I know I said that because that is my way of giving up on this problem...

OpenStudy (anonymous):

remember it in your heart!!!! rhombus with a right angle is a bloody SQUARE >:D okay, i'm overdoing things adventure? :)

OpenStudy (aric200):

Okay so it is A.. :?

OpenStudy (anonymous):

you're still not sure of yourself? :D

OpenStudy (aric200):

I want to be

OpenStudy (aric200):

Im sure that they all appear to look like squares

OpenStudy (aric200):

Not sure on what one MUST BE A SQUARE

OpenStudy (anonymous):

Sure enough, all of them COULD be squares but only one of them MUST be a square... and that's coz it's a rhombus with a 90 degree angle. It's A. Silly.

OpenStudy (aric200):

I said that and I gave my reason as to why I thought it was :/

OpenStudy (aric200):

I dislike you :D

OpenStudy (anonymous):

No you don't. :P

OpenStudy (aric200):

I believe @agent0smith deserves the medal over me :D

OpenStudy (anonymous):

fine.

OpenStudy (aric200):

:O nooooooooooooooo

OpenStudy (agent0smith):

@aric200 had the correct reasoning.

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