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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 8:23 am

A side question to the main question here.

If you know that AB=BC, can you say z=k?

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Source: Beat The GMAT — Data Sufficiency | Mon Jan 31, 2011 8:23 am

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Mon Jan 31, 2011 9:09 am

yes because the two trianle will be symmetric or same size

Charged up again to beat the beast

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 31, 2011 10:30 am

yellowho wrote:If you know that AB=BC, can you say z = k?

If AB = BC, then in âˆ†ABD and âˆ†CBD,

AB = BC
BD is common side
angle ABD = angle CBD = right angle

Hence, the triangle are congruent, i.e. the lengths of their corresponding sides and measures are corresponding angles are same. Hence, z = k. Also x = y.

For more details on congruent triangles, consult any standard geometry book or visit https://www.onlinemathlearning.com/congr ... ngles.html or https://staff.argyll.epsb.ca/jreed/math9 ... gruent.htm

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 9:59 pm

Thanks. Can you look at this similar problem. Here, AO=OC because both are radius but the answer suggests that you CANNOT assume that Z=Y because AO=OC. I know you are right and the answer is right so what am I missing here? What's the difference?

[quote="Anurag@Gurome"][quote="yellowho"]If you know that AB=BC, can you say z = k?[/quote]
If AB = BC, then in âˆ†ABD and âˆ†CBD,
[list]AB = BC
BD is common side
angle ABD = angle CBD = right angle[/list]
Hence, the triangle are congruent, i.e. the lengths of their corresponding sides and measures are corresponding angles are same. Hence, z = k. Also x = y.

For more details on congruent triangles, consult any standard geometry book or visit [url]https://www.onlinemathlearning.com/congr ... ngles.html[/url] or [url]https://staff.argyll.epsb.ca/jreed/math9 ... gruent.htm[/url][/quote]

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by Anurag@Gurome » Mon Jan 31, 2011 10:03 pm

yellowho wrote:What's the difference?

The difference is in the original problem, BD was perpendicular on AC, bu here OB is not perpendicular to AC.

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 10:06 pm

Got it thanks. So in a triangle if two sides are equal than its corresponding angles are equal and the converse. But here, since you essentially have two different triangles, you cant apply that rule?

[quote="Anurag@Gurome"][quote="yellowho"]What's the difference?[/quote]

The difference is in the original problem, BD was perpendicular on AC, bu here OB is not perpendicular to AC.[/quote]

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