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Rectangles.

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by prada » Wed Feb 17, 2016 4:56 pm
Hey Guys, at the risk of sounding dumb, I think I have some conceptual cognitive dissonance.

In a square if you have a diagonal it splits the square into two 45-45-90 triangles. Thus with with just the measure of one side or of the diagonal you can find the other, or the squares area, etc.

Now a diagonal in a rectangle splits the rectangle into two triangles down the middle too. Hence it should be a 45-45-90 triangle too? But then that would mean that you would have two equal sides and thus that rectangle is actually a square?

An example would be this, shouldn't angle B and D be both 45-45 and therefore it would mean its opposite sides should be equal as in AB=AD?

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by MartyMurray » Wed Feb 17, 2016 7:22 pm
prada wrote:In a square if you have a diagonal it splits the square into two 45-45-90 triangles. Thus with with just the measure of one side or of the diagonal you can find the other, or the squares area, etc.

Now a diagonal in a rectangle splits the rectangle into two triangles down the middle too. Hence it should be a 45-45-90 triangle too? But then that would mean that you would have two equal sides and thus that rectangle is actually a square?
Clearly it is not the case that every rectangle is a square. So you need to figure out where you have gone wrong. Maybe try visualizing or drawing various rectangles.

What if a rectangle were to have a very long length and a short width? Would the triangles formed by the diagonals still be 45-45-90 triangles?

Do the triangles in the image that you posted look like 45-45-90 triangles?

If the diagonals of a square form 45-45-90 triangles, what do the diagonals of a non square rectangle form?

You need to be able to see these kinds of things and to be adept at manipulating shapes in order to get some types of geometry questions right.
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by prada » Thu Feb 18, 2016 4:05 pm
Marty Murray wrote:
prada wrote:In a square if you have a diagonal it splits the square into two 45-45-90 triangles. Thus with with just the measure of one side or of the diagonal you can find the other, or the squares area, etc.

Now a diagonal in a rectangle splits the rectangle into two triangles down the middle too. Hence it should be a 45-45-90 triangle too? But then that would mean that you would have two equal sides and thus that rectangle is actually a square?
Clearly it is not the case that every rectangle is a square. So you need to figure out where you have gone wrong. Maybe try visualizing or drawing various rectangles.

What if a rectangle were to have a very long length and a short width? Would the triangles formed by the diagonals still be 45-45-90 triangles?

Do the triangles in the image that you posted look like 45-45-90 triangles?

If the diagonals of a square form 45-45-90 triangles, what do the diagonals of a non square rectangle form?

You need to be able to see these kinds of things and to be adept at manipulating shapes in order to get some types of geometry questions right.
Ahhh yeah I knew there was something I wasn't thinking and I need to think more of an atypical rectangular where my flawed thinking would expose itself. The angle above and under the diagonal should sum to 90 degrees but each part isn't necessarily 45 degrees. Only in a square would the two be 45 and hence the lengths would be identical too.

thx
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by [email protected] » Thu Feb 18, 2016 5:07 pm
Hi prada,

What is the source of this question? I ask because it appears to be a bastardized version of THIS question...

https://www.beatthegmat.com/geometry-t280370.html

...but whoever copied it didn't seem to understand what the original question was really about.

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by prada » Thu Feb 18, 2016 5:17 pm
[email protected] wrote:Hi prada,

What is the source of this question? I ask because it appears to be a bastardized version of THIS question...

https://www.beatthegmat.com/geometry-t280370.html

...but whoever copied it didn't seem to understand what the original question was really about.

GMAT assassins aren't born, they're made,
Rich
HI Rich,
Im not sure which is the original and which is the bastardized version. All I know is that I took a screen shot from
https://www.gmatprepnow.com/module/gmat ... /video/898

I did find the explanation a little long for a GMAT question but my question was more a conceptual one.
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by Matt@VeritasPrep » Thu Feb 18, 2016 5:57 pm
prada wrote: Ahhh yeah I knew there was something I wasn't thinking and I need to think more of an atypical rectangular where my flawed thinking would expose itself. The angle above and under the diagonal should sum to 90 degrees but each part isn't necessarily 45 degrees. Only in a square would the two be 45 and hence the lengths would be identical too.

thx
It's also worth remembering that there are many more subtle relationships between sides and angles than the GMAT expects you to know, so don't go too far down the rabbit hole with geometry. (Unless you like it, of course: it is fascinating!)
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Re: Rectangles.

by Johnsondavid » Thu Feb 20, 2025 7:43 pm
thank you so much
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