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Geom Question bank query

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jigar24
 Post subject: Geom Question bank query
 Post Posted: Tue Jun 16, 2009 3:37 am 
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Students


Posts: 57
In the Geom question bank, for DS question

If angle BAD is a right angle, what is the length of side BD?
(1) AC is perpendicular to BD

(2) BC = CD

Solution says:
Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD).

How can we say it’s an isosceles triangle? Is this a property? Please explain

Jigar
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Pankaj.Dahiya
 Post subject: Re: Geom Question bank query
 Post Posted: Sat Jun 20, 2009 11:15 am 
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Location: New Delhi, India
Lets call AC=h and BC=CD=x
Using Pythagoras, AB=AD=x^2+h^2
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j.vishal
 Post subject: Re: Geom Question bank query
 Post Posted: Sat Jul 04, 2009 3:15 am 
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As AC bisects BD, it would bisect angle BAD as well. So angle BAC= angle CAD = 45. As the triangles ABC and CAD are also rightangle triangles, so angle CBA and angle CDA would be 45 each.

The side of the triangle facing the equal angles are also same so BC=CD=AB=AD. Hence Triangle BAD is an isosceles triangle.

Thanks
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Ben Ku
 Post subject: Re: Geom Question bank query
 Post Posted: Fri Jul 31, 2009 1:51 am 
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ManhattanGMAT Staff


Posts: 824
Thanks j.vishal. That was a good explanation.

Another approach is to say that both right triangles ACB and ACD have two congruent legs, (AC = AC and CB = CD), then their hypotenuses are also congruent (AB = AD). BAD is isosceles.

Hope that helps!

_________________
Ben Ku
Instructor
ManhattanGMAT
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