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# Math: Polygons

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Director
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23 Aug 2010, 14:48
So Bunuel, if it is given that diagonals bisect then is it definitely a parallelogram? in other words it is a necessary and sufficient condition for parallelogram?

what is the difference between a trapezoid and trapezium? do the diagonals bisect in a trapezium?
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23 Aug 2010, 18:52
Thank You.Excellent post.
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24 Aug 2010, 00:48
mainhoon wrote:
Thanks for the post Bunuel. I have a doubt. Do the diagonals bisect each other in a trapezoid?

Bunuel wrote:
logan wrote:
nice post, as usual, Bunuel...

i m becoming a great fan of ur posts...

a small suggestion from my side... in the explanation of trapezoid, the diagram shows bases as a and b and height as h, but in the formula for area you considered different variables, though this doesn't point out any mistake in the formula, it would be clear if u considered the same variables...

with such wonderful posts gmatclub can start its own quant book i suppose.... wow...

i almost forgot.... kudossssssssss..... +1

Thanks. You are right, changed the variables as you suggested. +1 for good suggestion.

As for the quant book: actually we are working on our very own GMAT MATH BOOK. Of course much work has to be done till completing it: this topic isn't finished yet, we are working on Number Theory, other topics are waiting... But at the end we'll hope to get comprehensive guide to the quant topics of GMAT.

dear just see the link in Bunuel signatures ....the geometry notes(like other notes )are amazing ....take a print ...read one ce a day ... in a week you will be on top of all the properties

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29 Aug 2010, 21:47
Excellent post. thanks. You are amazing.
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30 Aug 2010, 13:23
excellent ! - thank you +1

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05 Oct 2010, 10:59
Thanks Bunuel for such comprehensive notes....

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07 Oct 2010, 19:46
Hi Bunuel,
Nice post can you extend this by including solid figures also.

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07 Oct 2010, 23:33
mission2009 wrote:
Hi Bunuel,
Nice post can you extend this by including solid figures also.

math-3-d-geometries-102044.html
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27 Nov 2010, 05:45
One more masterpiece from Bunuel...... Kudos...!!

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01 Feb 2011, 23:32
Pkit wrote:
Bunuel,

How many diagonals has a polygon with 25 sides?

the formula is:
Number of diagonals in a given polygon is =$$\frac{n*(n-3)}{2}$$, where n – is the number of sides.

simple example in a square number of diagonals is =$$\frac{4*(4-3)}{2}=2$$

The below is the concept used to derive the above formula for Number of diagonals .

As we know, to make a diagonal (a line), we need 2 (a pair of) points.
if i have n sided plygon, i need to select different par of points.

This can be doen in $$nc2$$ ways
but thease pairs include all the sides also. hence subtract the number of sides ($$n$$), whiich are not diagonals, from the above
==> $$The Number of diagonals$$ is
==> $$nc2-n$$
==> $$\frac{n(n-1)}{2} - n$$
==> $$\frac{(n^2-3n)}{2}$$
==> $$\frac{n(n-3)}{2}$$

Regards,
Murali.

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08 Feb 2011, 00:14
Great post , as always!, by Bunuel. Thanks

Great post !!! THANK YOU
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27 Jun 2011, 08:22
Hi, Super awesome post by the genius again.

One small doubt. if a DS question talks about a parallelogram and then goes on to say that the diagonals are equal. Does it imply we have a rectangle ?

Further the post says that should the diagonals of a parallelogram be equal and the angles be bisected by it, its a square. But I think this will happen in case of both a rect and a square ?
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27 Jun 2011, 08:24
Hi, Super awesome post by the genius again.

One small doubt. if a DS question talks about a parallelogram and then goes on to say that the diagonals are equal. Does it imply we have a rectangle ?

Further the post says that should the diagonals of a parallelogram be equal and the angles be bisected by it, its a square. But I think this will happen in case of both a rect and a square ?
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02 Jul 2011, 04:14
many thanks for this !

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15 Jul 2011, 23:22
Great post....Thanks

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17 Jul 2011, 04:22
great post..thanks Bunuel
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23 Jul 2011, 19:21
another awesome post... thanks Benuel
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Asher

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10 Nov 2011, 00:23
Many thanks!! could find the info only there!! highly appreciate

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03 Dec 2011, 12:25
Amazing post, thank you!

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03 Jan 2012, 23:28
Bunuel, thanks once again for your great work.

Although this has already been asked in some form on this thread, I would like to ask you to add a set of sufficient properties that would allow a GMAT taker to determine the type of a quad. I find that this aspect is very moot in the Manhattan Geometry guide. The set of properties should be as minimal as possible in order to be useful on DS questions. For example (please correct me if those properties are not true),

Parallelogram
Given a quad, if its opposite sides are parallel then it is a parallelogram.
Given a quad, it its opposite sides are equal then it is a parallelogram.

Rhombus
Given a quad, if its diagonals are perpendicular bisectors then it is a rhombus.

Square
Given a quad, if its sides are equal then it is a square.
Given a quad, if its angles are equal (90 degrees) then it is a square.
Given a quad, if its diagonals are equal then it is a square.

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Re: Math: Polygons   [#permalink] 03 Jan 2012, 23:28

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