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Re: The length of the side DC and AB
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26 May 2019, 07:26
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.