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If angle BAD is a right angle, what is the length of side BD

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jennifer.f.rizk
 Post subject: If angle BAD is a right angle, what is the length of side BD
 Post Posted: Sun Nov 15, 2009 7:00 pm 
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If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

In this question why is triangle BAD isoscles?-This is from the geometry question bank.
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Ben Ku
 Post subject: Re: If angle BAD is a right angle, what is the length of side BD
 Post Posted: Thu Dec 03, 2009 2:28 am 
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ManhattanGMAT Staff


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jennifer.f.rizk wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

In this question why is triangle BAD isoscles?-This is from the geometry question bank.


In this problem, you can infer BAD is isosceles ONLY from statement (2). Basically, AC splits the right triangle into two smaller triangles (ACB and ACD). Now these two triangles are congruent to each other, since they both share AC as one leg, and the other legs have equal lengths (BC=CD).

Since these two smaller triangles (ACB and ACD) are congruent, then their hypotenuses also have the same length (AB=AD). Therefore triangle BAD is an isosceles right triangle.

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carole.okigbo
 Post subject: Re: If angle BAD is a right angle, what is the length of side BD
 Post Posted: Thu Feb 18, 2010 11:31 am 
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great, thanks for the explaination
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Ben Ku
 Post subject: Re: If angle BAD is a right angle, what is the length of side BD
 Post Posted: Thu Feb 25, 2010 12:49 am 
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ManhattanGMAT Staff


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You're welcome!

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Ben Ku
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ManhattanGMAT
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