How to find if rhombuses are similar

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Math › How to find if rhombuses are similar

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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

I and II only

CORRECT

I and III only

0

II and III only

0

I, II, and III

0

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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