Parallelogram
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Not exactly but all quadrilaterals have 4 sides and 4 interior angles that add up to 360 degrees.
No. Two regular hexagons are always similar to each other, but two random hexagons are not necessarily similar.
A square, a rhombus and a kite are three examples of quadrilaterals that have perpendicular diagonals that intersect each other at right angles.
always
Similar shapes need to have the same number of sides, the same angles and the ratio of the sides needs to be the same. Rectangles are not always similar to each other because they can have different dimensions, which would break the "same ratio" rule.