Question

which of the following statements is false?
a. the diagonals of a rhombus are perpendicular and bisect each other.

b. in quadrilateral (pqrs), (angle p) and (angle s) are opposite angles.

c. a rhombus is a quadrilateral.

d. a quadrilateral is a polygon with four angles.

reset selection

Explanation:

• Option A: A defining property of a rhombus is that its diagonals are perpendicular and bisect each other, so this is true.
• Option B: In quadrilateral \(PQRS\), the vertices are ordered, so adjacent angles are \(\angle P\) & \(\angle Q\), \(\angle Q\) & \(\angle R\), \(\angle R\) & \(\angle S\), \(\angle S\) & \(\angle P\). Opposite angles are \(\angle P\) & \(\angle R\), \(\angle Q\) & \(\angle S\). Thus, \(\angle P\) and \(\angle S\) are adjacent, not opposite, making this false.
• Option C: A rhombus has four sides, so it is a quadrilateral, this is true.
• Option D: A quadrilateral is a 4-sided polygon, which has four interior angles, so this is true.

Answer:

B. In quadrilateral \(PQRS\), \(\angle P\) and \(\angle S\) are opposite angles.