Quadrilaterals

The properties of parallelograms, rectangles, rhombuses and squares, and the mid-point theorem for triangles.

Key ideas

• The angles of any quadrilateral add up to 360°.
• In a parallelogram, opposite sides are equal, opposite angles are equal, and the diagonals bisect each other.
• Neighbouring angles of a parallelogram add up to 180°.
• A rectangle is a parallelogram with equal diagonals; a rhombus has diagonals that bisect each other at right angles.
• A square has all of these: equal sides, right angles, and equal diagonals at right angles.
• Mid-point theorem: the line joining the midpoints of two sides of a triangle is parallel to the third side and half as long.

Remember

Watch out

• Assuming a rhombus has equal diagonals (only if it is a square).
• Saying the diagonals of every parallelogram are perpendicular.
• Doubling instead of halving in the mid-point theorem.

Worked example