True. All rectangles are trapezoids.
(In England a trapezoid is known as a trapezium.)
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No. A trapezoid must have two parallel sides and two non-parallel sides. A rectangle must have two sets of two parallel sides and all angles of 90o. The two terms are mutually exclusive.
Both trapezoids and rectangles are quadrilaterals.
how are trapezoids and rectangles
squares and rectangles
Squares, parallelograms, rhombuses, and trapezoids are quadrilaterals that are not rectangles.
Certain quadrilaterals have right angles. Right trapezoids are the most general example. Rectangles are specialized right trapezoids, and squares are specialized rectangles. There may be more but I can't recall them. Many rhombuses and parallelograms have no right angles. However, they might (and then you'd probably call them squares or rectangles but they are also technically rhombuses, parallelograms and trapezoids).