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Trapezoid In Triangle

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bruno.torres.gomez
 Post subject: Trapezoid In Triangle
 Post Posted: Sun Mar 20, 2011 5:59 am 
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Students


Posts: 5
In one of the MGMAT CAT tests, i found this

If BE CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?
.A
/ \
B/___ \ E
/ \
c---------D

... using proportions > AD = 8

In the answer, it states ->

Triangle CAD is a right triangle since it has side lengths of 6, 8 and 10, which means that triangle BAE is also a right triangle (they share the same right angle).

Can the sides determine the type of triangle ? (in this case, it is a triangle rectangle because of 6,8 and 10) i read somewhere, that it cannot ? So, if i see a triangle 2,1,1*sqrt(3) , then it must be a 30-60-90 ?

Please do let me know
Very much appreciated .

Bruno
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jnelson0612
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Sun Mar 20, 2011 3:21 pm 
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ManhattanGMAT Staff


Posts: 1857
Bruno, can you please post an image for this problem?

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Jamie Nelson
ManhattanGMAT Instructor
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bruno.torres.gomez
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Mon Mar 21, 2011 12:46 am 
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Students


Posts: 5
Hi,

Thanks for your reply!
Please see the image here (http://postimage.org/image/2gqmzti3o/)
Image
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tim
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Mon Mar 21, 2011 8:46 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
yes, if you have the three side lengths - or even the ratio of side lengths - you can determine all the angles of a triangle. in particular, if the sides of the triangle satisfy the Pythagorean Theorem you can conclude that the triangle is a right triangle..

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Tim Sanders
Manhattan GMAT Instructor
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bruno.torres.gomez
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Mon Mar 21, 2011 12:07 pm 
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Students


Posts: 5
thank you guys!
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jnelson0612
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Fri Apr 01, 2011 1:01 pm 
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ManhattanGMAT Staff


Posts: 1857
Thanks! :-)

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Jamie Nelson
ManhattanGMAT Instructor
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rgaddam
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Mon Apr 18, 2011 11:15 pm 
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Students


Posts: 14
tim wrote:
yes, if you have the three side lengths - or even the ratio of side lengths - you can determine all the angles of a triangle.


Can you please give me an example or two for the above statement so that I can better understand the concept.

Thanks
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tim
 Post subject: Re: Trapezoid In Triangle
 Post Posted: Tue Apr 26, 2011 2:00 pm 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
Bruno already gave you two examples..

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Tim Sanders
Manhattan GMAT Instructor
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