Which statement is false

Which statement is false?

All squares are rectangles.

All rhombuses are squares.

All squares are parallelograms.

All rhombuses are parallelograms.

The correct answer and explanation is:

The false statement is: All rhombuses are squares.

Explanation:

In geometry, understanding the relationships between different types of quadrilaterals is essential. Each of the statements deals with specific properties and classifications of shapes such as squares, rectangles, rhombuses, and parallelograms.

1. All squares are rectangles.
   This statement is true. A rectangle is defined as a quadrilateral with four right angles. A square has four right angles and four equal sides. Since a square meets all the criteria of a rectangle (four right angles), every square is also a rectangle. However, not all rectangles are squares because rectangles do not require all sides to be equal.
2. All rhombuses are squares.
   This statement is false. A rhombus is a quadrilateral with all four sides of equal length, but its angles are not necessarily right angles. For a rhombus to be a square, it must have four equal sides and four right angles. Therefore, while every square is a rhombus because it has equal sides, not every rhombus is a square. Many rhombuses have angles that are not 90 degrees.
3. All squares are parallelograms.
   This statement is true. A parallelogram is a quadrilateral where opposite sides are parallel and equal in length. Since a square has all four sides equal and opposite sides parallel, it fits the definition of a parallelogram. Therefore, every square is a parallelogram.
4. All rhombuses are parallelograms.
   This statement is true. A rhombus has all four sides equal and opposite sides are parallel. This matches the definition of a parallelogram, which requires opposite sides to be parallel. Hence, every rhombus is a parallelogram.

In summary, the key difference lies in angle properties. Squares have all right angles, while rhombuses only require equal side lengths. This makes the statement “All rhombuses are squares” false because not all rhombuses have right angles.