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what is the area of trapezoid BEDC?

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what is the area of trapezoid BEDC?

by gmattesttaker2 » Tue Feb 04, 2014 8:21 pm
Hello,

Can you please assist with this:

If BE || CD, and BC = AB = 3, AE = 4 and CD = 10, what is the area of trapezoid BEDC?

OA: 18


The official explanation says:

Since BE || CD, triangle ABE is similar to triangle ACD (parallel lines imply two sets of equal angles). The MGMAT book has the following definition for similar triangles:

"Triangles are defined as similar if all their corresponding angles are equal and their corresponding sides are in proportion."

So I was a bit confused as to how the two triangles ABE and ACD are similar just because BE is parallel to CD. Many thanks for your help.


Best Regards,
Sri
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by Bill@VeritasPrep » Wed Feb 05, 2014 12:02 am
A big triangle with a second parallel base is a pretty common way for the GMAT to test similar triangles. I actually just went over this in class tonight.

Using the Angle-Angle-Angle theorem:

1. Angle A is shared
2 Angles B and C are equal
3. Angles E and D are equal
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