Special quadrilaterals

Edexcel routinely asks for properties of named quadrilaterals — particularly on Foundation. Knowing each is essential for angle, area, and reasoning questions.

Square

• 4 equal sides; 4 right angles.
• Both pairs of opposite sides parallel.
• Diagonals: equal, bisect each other at 90°, bisect angles.
• Lines of symmetry: 4. Rotational symmetry: order 4.

Rectangle

• Opposite sides equal and parallel; 4 right angles.
• Diagonals equal and bisect each other (but not at 90° unless square).
• Lines of symmetry: 2. Rotational symmetry: order 2.

Rhombus

• 4 equal sides; opposite sides parallel.
• Opposite angles equal.
• Diagonals bisect each other at 90°; bisect angles.
• Lines of symmetry: 2. Rotational symmetry: order 2.

Parallelogram

• Opposite sides equal and parallel.
• Opposite angles equal; co-interior angles sum to 180°.
• Diagonals bisect each other (but not at 90°, not equal in general).
• Lines of symmetry: 0. Rotational symmetry: order 2.

Trapezium

• Exactly one pair of parallel sides (Edexcel's definition).
• Co-interior angles between the parallels sum to 180°.

Isosceles trapezium

• Trapezium with the non-parallel sides equal.
• Diagonals equal; one line of symmetry.

Kite

• Two pairs of adjacent equal sides (different from rhombus, where all four are equal).
• One pair of equal angles (the angles between unequal sides).
• Diagonals: one bisects the other at 90°.
• Lines of symmetry: 1.

Edexcel exam tip

When asked "name this quadrilateral", look at:

1. Which sides are equal (all 4? two pairs adjacent? two pairs opposite?).
2. Which sides are parallel (both pairs? one pair? none?).
3. Whether any angle is right.

Use these to narrow down systematically.

Quadrilateral angle sum

All quadrilaterals have angles summing to 360°. ("Angles in a quadrilateral sum to 360°".)