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As the figure below shows, line AE bisects

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by Max@Math Revolution » Fri Feb 07, 2020 1:07 am
[GMAT math practice question]

As the figure below shows, line AE bisects ∠A, line BE bisects ∠B, line CG bisects ∠C, and line DG bisects ∠D. What kind of quadrilateral is ABCD?
2.7PS.png
A. rhombus with acute inner angles
B. square
C. parallelogram with acute inner angles
D. rectangle
E. parallelogram with obtuse inner angles
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Re: As the figure below shows, line AE bisects

by Max@Math Revolution » Mon Feb 10, 2020 12:56 am
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Since quadrilateral ABCD is a parallelogram, ∠A + ∠B = 180 o, ∠EAB = (1/2)∠A, ∠EBA = (1/2) ∠B and ∠EAB + ∠EBA = (1/2)( ∠A + ∠B) = (1/2)(180 ) 90.
Thus ∠AEB = 90.
We have ∠EHG = ∠HGF = ∠EFG = 90 in similar ways.
Then, quadrilateral EFGH is a rectangle.

Therefore, D is the answer.
Answer: D
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