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Geometry

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Source: — Quantitative Reasoning |
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by Jim@StratusPrep » Thu Jan 17, 2013 10:32 am
They will both be 24. You will not have to use this application of angles on the GMAT, though.
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by Tommy Wallach » Fri Jan 18, 2013 6:47 pm
Hey Guys,

Just wanted to weigh in on this. This particular geometry issue IS tested on the GMAT. It's actually just the rule that equal sides are opposite equal angles.

Because Triangle BCD is an equilateral triangle, all the sides are the same (BD=BC=CD). Next, because Angle A = Angle B, AD = BD, which means AD = DC.

That means the two triangles (ABD and BDC) have the same base (AD and DC) and the same height. So their areas are equal.

-t

P.S. To see the actual GMAT play with this trick, see Question 123 from the second edition of the Quant Official Guide.
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by BTG14 » Fri Jan 25, 2013 9:09 pm
Hi Tommy,

Did you conclude AD = BD because opposite angles are equal and in same way did you conclude AD=DC
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by Tommy Wallach » Fri Jan 25, 2013 10:39 pm
Hey BTG,

That's absolutely right! Do the follow-up steps make sense to you?

-t
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