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Which is greater The length of the side DC

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Which is greater The length of the side DC [#permalink] New post 25 May 2019, 11:18
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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.
[Reveal] Spoiler: OA
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Re: The length of the side DC and AB [#permalink] New post 26 May 2019, 07:26
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Expert's post
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.
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Re: The length of the side DC and AB [#permalink] New post 08 Nov 2019, 16:08
MyGuruStefan Array[WROTE]:
Since, ∠DAB = x, then ∠ADB also is equal to x.


I wasn't sure how we can establish that ∠ADB = x.
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Re: The length of the side DC and AB [#permalink] New post 10 Nov 2019, 07:56
Expert's post
We know from the rule stating that the exterior angle of a triangle = sum of the opposite interior angles that ∠DBC or 2x = ∠DAB + ∠ADB. Since, ∠DAB = x solve the equation to find that ∠ADB also = x. Hope this helps!
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Re: Which is greater The length of the side DC [#permalink] New post 11 Nov 2019, 13:51
Nice post
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Re: Which is greater The length of the side DC [#permalink] New post 11 Nov 2019, 13:52
this explanatiom made my year
Re: Which is greater The length of the side DC   [#permalink] 11 Nov 2019, 13:52
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Which is greater The length of the side DC

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