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

by jennifer.f.rizk Sun Nov 15, 2009 7:00 pm

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

by Ben Ku Thu Dec 03, 2009 2:28 am

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

by carole.okigbo Thu Feb 18, 2010 11:31 am

great, thanks for the explaination
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Re: If angle BAD is a right angle, what is the length of side BD

by Ben Ku Thu Feb 25, 2010 12:49 am

You're welcome!
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Re: If angle BAD is a right angle, what is the length of side BD

by zdgura Wed Feb 29, 2012 10:35 pm

The correct answer to this is C. Ben your logic (and I apologize if I'm incorrect here) seems to make me think that B would suffice as an answer. Is C the correct answer because while stem 2 lets you know that you have two sides that are the same you don't know whether you have any angles that are the same. Stem 1 lets you know that the two are right triangles and you know have two sides being equal and you have angle information as well....is that correct?
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Re: If angle BAD is a right angle, what is the length of side BD

by tim Tue Mar 06, 2012 8:43 am

You're right. 2 alone is not sufficient to conclude that the triangle is isosceles. You need both statements..
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Re: If angle BAD is a right angle, what is the length of side BD

by lj6871849 Thu Aug 30, 2012 4:29 am

Hi Tim - one petite doubt.

Since AC is perpendicular to BD do we know the angle split at A is 45-45?

or is it because AC is perpendicular bisector do we know the angles formed at A by the like AC is 45-45?

Basically what i mean to ask is if we know AC is perpendicular to BD then do we know angle at is 45-45?
OR
If we know AC is perpendicular bisector of BD then do we know the angles formed at right angle A by AC is 45 degrees each?

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

by jlucero Thu Aug 30, 2012 6:11 pm

The second one. Otherwise this couldn't happen:
Attachments
tri.gif
tri.gif (2.27 KiB) Viewed 5977 times
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Re: If angle BAD is a right angle, what is the length of side BD

by SoumyaA472 Tue Feb 24, 2015 4:55 am

I came across this question in the Geometry question bank, so thought it is easier to post on an existing thread.
I was wondering why the 3 triangles are not similar based on A alone? Angle BAD = BCA = ACD = 90 degrees.

And based on this information and the side AD= 5 (given) , we should be able to determine the length of BD.
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Re: If angle BAD is a right angle, what is the length of side BD

by tim Sat Feb 28, 2015 9:01 pm

Can you post a screen shot of the relevant diagram so other students will be able to benefit from our answer? I see there was supposed to be an attachment in a previous post, but I can't access it.
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Re: If angle BAD is a right angle, what is the length of side BD

by AliasgharA585 Thu Jul 23, 2015 1:20 am

Hi
I just wanted to know if statement 1 would be sufficient since if AC is the perpendicular bisector then we know that it is 45-45-90 triangle and one side AD is known.From that we can calculate AC and similarly in triangle ACD which is a 45-45-90 triangle and side AC is known and can calculate side BC?
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Re: If angle BAD is a right angle, what is the length of side BD

by RonPurewal Sun Jul 26, 2015 6:43 am

can you please post a picture of the diagram? thanks.
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Re: If angle BAD is a right angle, what is the length of side BD

by RonPurewal Sun Jul 26, 2015 6:45 am

in any case-- if BAD is a RANDOM right triangle, then AC (in statement 1) is not necessarily a perpendicular BISECTOR.

to see this, just draw a triangle BAD that is decidedly NOT isosceles—e.g., draw a 10º-80º-90º triangle (or suchlike).
then draw the perpendicular.
you'll notice that it's not even close to being a bisector. (if 'D' is the smaller angle, then CD is going to be WAY longer than CA.)
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Re: If angle BAD is a right angle, what is the length of side BD

by AliasgharA585 Wed Jul 29, 2015 6:50 am

Thanks Ron for the explanation... :)
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Re: If angle BAD is a right angle, what is the length of side BD

by tim Tue Aug 04, 2015 11:04 am

Glad it helped!
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