Question

which of the following statements is false? select the best answer from the choices provided. a. all parallelograms are trapezoids. b. all rectangles are squares. c. all squares are rhombuses. d. all rhombuses are parallelograms.

Explanation:

• Option A: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. A parallelogram has two pairs of parallel sides. So, all parallelograms are trapezoids.
• Option B: A rectangle has four right - angles and opposite sides equal. A square has four right - angles, four equal sides. Not all rectangles have four equal sides. So, not all rectangles are squares.
• Option C: A rhombus has four equal sides. A square has four equal sides and four right - angles. So, all squares are rhombuses (a special type of rhombus with right - angles).
• Option D: A parallelogram has two pairs of parallel sides. A rhombus has two pairs of parallel sides (in addition to having four equal sides). So, all rhombuses are parallelograms.

Answer:

B. All rectangles are squares.