Question

which of the following statements is true? all rectangles are rhombuses. all rhombuses are parallelograms. a trapezoid must not have congruent sides. some trapezoids are parallelograms.

Explanation:

• A rectangle has four right angles but its adjacent sides are not necessarily equal (a rhombus has all sides equal). So "All rectangles are rhombuses" is false.
• A rhombus has two pairs of parallel sides. By the definition of a parallelogram (a quadrilateral with two pairs of parallel sides), all rhombuses are parallelograms.
• An isosceles trapezoid has congruent non - parallel sides. So "A trapezoid must not have congruent sides" is false.
• A trapezoid has exactly one pair of parallel sides, while a parallelogram has two pairs of parallel sides. So "Some trapezoids are parallelograms" is false.

Answer:

All rhombuses are parallelograms.