In a rectangle, the diagonals are equal in length but are not necessarily perpendicular.

In a rectangle, the diagonals are equal in length.

In a kite, the diagonals bisect each other but are not equal in length.

A kite has diagonals that are not equal in length, while the others have equal diagonals.

A kite has diagonals that are not equal, which distinguishes it from squares, rectangles, and rhombuses.

In a rhombus, the diagonals bisect each other at right angles.

A trapezium is defined as a quadrilateral with at least one pair of parallel sides.

A parallelogram is defined as a quadrilateral with opposite sides that are both equal and parallel.

A rhombus has opposite sides that are equal and parallel, making it a special type of parallelogram.

A square has equal diagonals, which is a property of squares and rectangles.

A triangle is a polygon as it is a closed figure with straight sides.

In a kite, one pair of opposite angles are equal, while the other properties do not hold true.

In a parallelogram, the diagonals bisect each other, which is a defining property of parallelograms.

In a rectangle, all angles are right angles and opposite sides are equal, but not all sides are equal.

In a rectangle, opposite sides are equal and all angles are indeed 90 degrees.

In a rhombus, while all sides are equal and diagonals bisect at right angles, not all angles are right angles.

In a rhombus, while all sides are equal and diagonals bisect each other at right angles, the diagonals are not equal in length.

While the diagonals of a square are equal and bisect each other, they are not necessarily perpendicular to each other in all quadrilaterals.

In an equilateral triangle, all sides are equal and all angles measure 60 degrees.

Linear pairs are not equal; they are supplementary, meaning they add up to 180 degrees.

Linear pairs of angles formed by intersecting lines are always supplementary, meaning they add up to 180 degrees.

Angles subtended by the same arc at the circumference of a circle are equal.

The area of a regular polygon can indeed be calculated using the formula A = (1/4) * n * s^2 * cot(π/n), where n is the number of sides and s is the side length.

A triangle has no diagonals, as it has only three vertices. The formula for the number of diagonals in a polygon is n(n-3)/2, where n is the number of sides.

The number of diagonals in a polygon is calculated using the formula n(n-3)/2, where n is the number of sides.

The sum of the angles in any triangle is always 180 degrees, which is a fundamental property of triangles.

Polygons are defined as shapes with straight sides, so a polygon cannot have curved sides.

A regular hexagon has all sides and angles equal, making the statement true.

A regular polygon has both equal sides and equal angles, making both statements true.

In an equilateral triangle, all sides are equal and all angles are equal, each measuring 60 degrees.