What do all rhombuses have in common?
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Answer

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Step 1:
I'll solve this problem step by step, focusing on the key properties of rhombuses:

Step 2:
: Definition of a Rhombus

A rhombus is a quadrilateral with four equal-length sides. This is the most fundamental characteristic that all rhombuses share.

Step 3:
: Side Length Property

\overline{AB} = \overline{BC} = \overline{CD} = \overline{DA}
This means all sides of a rhombus are congruent (equal in length).

Step 4:
: Symmetry Properties

All rhombuses have: - Two pairs of parallel sides - Two lines of symmetry (diagonals bisect each other) - Rotational symmetry of 180 degrees

Step 5:
: Diagonal Characteristics

- Diagonals bisect each other at their midpoint - Diagonals bisect the angles of the rhombus - Diagonals are not equal in length (unless it's a square)

Step 6:
: Angle Properties

- The sum of adjacent angles is always $$180^\circ
- Opposite angles are congruent

Final Answer

All rhombuses have four equal-length sides, two pairs of parallel sides, diagonals that bisect each other, and symmetrical properties that distinguish them from other quadrilaterals.