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Example Question #1 : How To Find If Rhombuses Are Similar
A quadrilateral ABCD has diagonals that are perpendicular bisectors of one another. Which of the following classifications must apply to quadrilateral ABCD?
I. parallelogram
II. rhombus
III. square
Possible Answers:
I and III only
I, II, and III
I and II only
II and III only
Correct answer:
I and II only
Explanation:
If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.
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