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Source: Beat The GMAT — Data Sufficiency |
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Anurag@Gurome
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If AB = BC, then in ∆ABD and ∆CBD,yellowho wrote:If you know that AB=BC, can you say z = k?
- AB = BC
BD is common side
angle ABD = angle CBD = right angle
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
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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 ∆ABD and ∆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]
[quote="Anurag@Gurome"][quote="yellowho"]If you know that AB=BC, can you say z = k?[/quote]
If AB = BC, then in ∆ABD and ∆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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Anurag@Gurome
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The difference is in the original problem, BD was perpendicular on AC, bu here OB is not perpendicular to AC.yellowho wrote:What's the difference?
Anurag Mairal, Ph.D., MBA
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yellowho
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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]
[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]
