State true/false:

Every kite is a rhombus.

False

Explanation:

To understand why the statement Every kite is a rhombus is false, let's examine the definitions and properties of both shapes:

Definitions

Kite: A quadrilateral with two distinct pairs of adjacent sides that are equal in length. In a kite:

• The diagonals are perpendicular to each other.
• One diagonal bisects the other.
• One pair of opposite angles (where the unequal sides meet) are equal.

Rhombus: A quadrilateral where all four sides are of equal length. In a rhombus:

• Opposite sides are parallel.
• Opposite angles are equal.
• The diagonals are perpendicular bisectors of each other.
• The diagonals bisect the interior angles.

Key Differences

Side Lengths:

• In a kite, there are two pairs of adjacent sides that are equal, but the four sides are not necessarily of the same length.
• In a rhombus, all four sides are of equal length.

Angles:

• A kite has one pair of equal opposite angles.
• A rhombus has both pairs of opposite angles equal.

Diagonals:

• In a kite, one diagonal bisects the other at a right angle.
• In a rhombus, both diagonals bisect each other at right angles and are axes of symmetry.

While a rhombus satisfies all the properties of a kite (making every rhombus a kite), the converse is not true. Not all kites have four sides of equal length or the specific angle properties of a rhombus. Therefore, the statement "Every kite is a rhombus" is false.