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Which is greater The length of the side DC
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25 May 2019, 11:18
25 May 2019, 11:18
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Question Stats:
38% (01:29) correct
61% (01:40) wrong based on 57 sessions
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Quantity A |
Quantity B |
The length of side DC |
The length of side AB |
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.
GRE Prep Club Tests Editor
Joined: 13 May 2019
Affiliations: Partner at MyGuru LLC.
Posts: 186
Given Kudos: 5
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE:Education (Education)
Re: The length of the side DC and AB
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26 May 2019, 07:26
26 May 2019, 07:26
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Expert Reply
For geometry Quantitative Comparisons, look for ways to relate information algebraically.
For this problem, we first know that the exterior angle of any triangle = sum of two opposing interior angles.
Therefore, 2x = ∠DAB + ∠ADB. Since, ∠DAB = x, then ∠ADB also is equal to x.
Furthermore, we know that according to the proportionality rules of triangles, sides opposing equal angles in a triangle are also equal.
Therefore, because ∠DCB = ∠DBC = 2x, the opposing sides DB and DC must also be equal.
Finally, because ∠DAB = ∠ADB = x, the opposing sides DB and AB must also be equal.
Using the transitive property determine that AB = DB = DC. The quantities are equal, so select Choice C.
For this problem, we first know that the exterior angle of any triangle = sum of two opposing interior angles.
Therefore, 2x = ∠DAB + ∠ADB. Since, ∠DAB = x, then ∠ADB also is equal to x.
Furthermore, we know that according to the proportionality rules of triangles, sides opposing equal angles in a triangle are also equal.
Therefore, because ∠DCB = ∠DBC = 2x, the opposing sides DB and DC must also be equal.
Finally, because ∠DAB = ∠ADB = x, the opposing sides DB and AB must also be equal.
Using the transitive property determine that AB = DB = DC. The quantities are equal, so select Choice C.
Re: The length of the side DC and AB
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08 Nov 2019, 16:08
08 Nov 2019, 16:08
MyGuruStefan wrote:
Since, ∠DAB = x, then ∠ADB also is equal to x.
I wasn't sure how we can establish that ∠ADB = x.
