If a quadrilateral has all its vertices on the circle and its opposite angles are supplementary (here x+y = 180°), then that quadrilateral is called a cyclic quadrilateral.
- In a cyclic quadrilateral, the opposite angles are supplementary
- Area of a cyclic quadrilateral is $$A$$ = $$\sqrt{(s-a)(s-b)(s-c)(s-d)} $$ where s=(a+b+c+d)/2
- The exterior angle is equal to the opposite angle of its remote interior angle. (here ∠CBX = ∠ADC)
- Area = 1/2 * One diagonal * Sum of perpendiculars drawn to the diagonal
- Ptolemy's theorem states that the product of the diagonals equals the sum of the products of the opposite sides. AC*BD = AB*CD + AD*BC.
- Rectangle: Area = l × b, Diagonal = $$\sqrt{(l² + b²)}$$.
- Square: Area = a², Diagonal = a$$\sqrt{2}$$.
- Rhombus: Side = $$\sqrt{((d₁/2)² + (d₂/2)²)}$$.
- Median of a trapezium (mid-segment) = (sum of parallel sides)/2.
- For a trapezium, Area = 1/2 * sum of parallel sides * distance between them.
- For a parallelogram, Area = Base * Height = Product of two sides * sine of the included angle.
- For a rhombus, Area = 1/2 * Product of diagonals.
- The sum of the three sides of a quadrilateral must be greater than the fourth side.
