Key Properties of Quadrilaterals

Key Properties of Quadrilaterals

• Opposite sides of a rectangle are always parallel.
• Adjacent sides of a rhombus are always congruent.
• Diagonals of a rhombus are sometimes congruent.
• Opposite sides of a parallelogram are always congruent.
• Diagonals of a rectangle are sometimes perpendicular.
• Diagonals of a rectangle always bisect opposite angles.
• Opposite angles of a parallelogram are sometimes congruent.
• Consecutive angles of a parallelogram are sometimes congruent.
• Diagonals of a parallelogram always bisect each other.
• The four angles of a rhombus are sometimes right angles.
• Consecutive sides of a rhombus are always congruent.

Quadrilaterals and Parallelograms

• Diagonals of a quadrilateral sometimes bisect each other.
• If two angles of a quadrilateral are equal, the quadrilateral is sometimes a parallelogram.
• If both pairs of opposite sides of a quadrilateral are congruent, it is always a parallelogram.
• A sufficient condition to prove a quadrilateral is a parallelogram is never achieved by showing one pair of opposite sides is parallel.
• If both pairs of opposite angles of a quadrilateral are congruent, it is always a parallelogram.

Special Quadrilaterals

• A square is always a rhombus.
• A quadrilateral is sometimes a parallelogram.
• A rectangle is sometimes a rhombus.
• A parallelogram with at least one right angle is sometimes a square.
• A trapezoid is never a parallelogram.
• A quadrilateral is sometimes a trapezoid.
• The bases of an isosceles trapezoid are never congruent.
• A parallelogram is sometimes a rectangle.
• A kite has congruent diagonals never.

Triangle Properties in Quadrilaterals

• Each diagonal of a parallelogram always divides it into two congruent triangles.
• A parallelogram whose diagonals are congruent and perpendicular to each other is always a square.
• A quadrilateral can sometimes be a parallelogram if its diagonals are perpendicular.
• The bases of a trapezoid are never congruent.
• Opposite angles of a parallelogram are sometimes supplementary.
• If the diagonals of a quadrilateral are perpendicular, the quadrilateral is sometimes a square.
• A diagonal of an isosceles trapezoid never divides it into two congruent triangles.
• A rhombus is sometimes equiangular.
• A quadrilateral with congruent angles is always a rectangle.
• If the diagonals of a square are drawn, the resulting four triangles are always isosceles right triangles.
• If the diagonals of a parallelogram bisect opposite angles, the parallelogram is sometimes a square.