yes - all the rhombuses. By definition a trapezoid has two parallel sides, a rhombus also has two parallel sides - because both pairs of opposite sides are parallel. So all rhombuses are trapezoids (but not all trapezoids are rhombuses)
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No. Rhombuses that are also rectangles are called squares. Rhombuses are parallelograms with 4 equal sides, while rectangles are parallelograms where all the angles are right.
Quadrilaterals are things with four sides, like squares, rectangles, diamonds, trapezoids, rhombuses. Anything that doesn't have four sides (an infinite list) is a non-example of a quadrilateral.
No trapezoids are parallelograms, and no parallelograms are trapezoids.
A rhombus is a quadrilateral in which all of the sides are of equal length, It is an equilateral quadrangle. If any angle of an equilateral quadrangle is a right angle, then all its angles are right angles. It is also a square. All squares are rhombuses. Some rhombuses are squares. A rhombus is a parallelogram with 4 congruent sides. A square is a rhombus with 4 congruent angles.
There are isosceles trapezoids which are sometimes called regular trapezoids.