Some have symmetry , but not all !!!
Square, Rectangle, Rhombus, Kite all have symmetry.
A trapezium can be both asymmetric, and symmetric.
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A square
Types of quadrilaterals that have lines of symmetry: squares, rectangles, some rhombuses (standard diamond shape), boomerang shape, and trapezoids.
trapezoid for one
There are two quadrilaterals with 2 lines of symmetry. A rhombus and a rectangle (if they are not also a square)
Different quadrilaterals have different lines of symmetry, try searching a specific shape for example square