How is a rhombus defined in geometry?

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Detailed Solution

In Euclidean geometry, a rhombus is defined as a quadrilateral (a four-sided polygon) where all four sides have the exact same length. Because its sides are all equal, it is also known as an equilateral quadrilateral.

This single definition leads to several other important properties:

It is a Parallelogram: A rhombus is a special type of parallelogram, which means its opposite sides are parallel to each other.
Opposite Angles are Equal: The two opposite acute (pointy) angles are equal, and the two opposite obtuse (wide) angles are equal.
Consecutive Angles are Supplementary: Any two angles next to each other add up to 180 degrees.
Diagonals Bisect Each Other: The two diagonals (lines connecting opposite corners) cross at their midpoints.
Diagonals are Perpendicular: The diagonals intersect at a perfect 90-degree (right) angle.
Diagonals Bisect Angles: Each diagonal cuts the corner angles it passes through into two equal halves.

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