Yes.
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Yes because all 4 sided shapes are quadrilaterals which includes trapezoids.
No because a trapezoid only has 1 pair of parallel sides whereas a parallelogram has 2 pairs of parallel sides but they are both 4 sided quadrilaterals.
No trapezoids are not parallelograms. Trapezoids are actually quadrilaterals and they have one pair of opposite sides. Parallelograms by definition have 2 pairs of parallel sides.
Types of quadrilaterals that have lines of symmetry: squares, rectangles, some rhombuses (standard diamond shape), boomerang shape, and trapezoids.
Trapezoids have only one pair of parallel sides. A parallelogram has two pair of parallel sides.