4.8 Summary
Key Points
- A rectangle is a quadrilateral with all angles 90^\circ. Its opposite sides are equal and parallel; its diagonals are equal and bisect each other.
- A square has all angles 90^\circ and all sides equal. Its diagonals are equal, bisect each other at 90^\circ, and bisect the corner angles.
- A parallelogram has both pairs of opposite sides parallel. Opposite sides are equal, opposite angles equal, adjacent angles sum to 180^\circ, and the diagonals bisect each other (though generally unequal). Conversely, if a quadrilateral’s diagonals bisect each other, it is a parallelogram.
- A rhombus has all four sides equal. It is a parallelogram whose diagonals also meet at 90^\circ and bisect the corner angles.
- A kite has two adjacent pairs of equal sides; one diagonal is its axis of symmetry, bisecting two angles and meeting the other diagonal perpendicularly at its midpoint.
- A trapezium has at least one pair of parallel sides; an isosceles trapezium has equal slant sides and equal base angles.
- Any quadrilateral has angle sum 360^\circ.
- Every square is a rectangle and a rhombus; every rectangle and rhombus is a parallelogram; every rhombus is a kite; every parallelogram is a trapezium.
- Joining the midpoints of the sides of any quadrilateral always produces a parallelogram.