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the ratio of the length of line segment
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09 Aug 2022, 07:28
09 Aug 2022, 07:28
Expert Reply
2
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Question Stats:
85% (01:41) correct
14% (00:36) wrong based on 7 sessions
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Attachment:
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Quantity A |
Quantity B |
the ratio of the length of \(\frac{line segment AB}{the length of line segment DB}\) to the ratio of \(\frac{the length of line segment AE}{the length of line segment DC}\) |
\(\frac{3}{4}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Part of the project: GRE Quantitative Comparison GEOMETRY+Tricky Questions - Special Summer Edition (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
the ratio of the length of line segment
[#permalink]
10 Aug 2022, 00:12
10 Aug 2022, 00:12
Expert Reply
OE
Quote:
∠1 and ∠2 are vertical angles, and therefore congruent, so ∠1 measures 75°. This can be used to determine the measure of the third angle of each triangle and consequently that triangles ABE and CBD are similar by Angle-Angle. The lengths of two corresponding sides of similar triangles are always proportionate, so the ratio in column A works out to 1/1>3/4 so the answer is a. This problem is easy to solve if you know the properties of similar triangles and are able to understand the ratio described in column A.
