Duality in Quadrilaterals
As an example of the side-angle duality of polygons we compare properties of the cyclic and tangential quadrilaterals.
| Cyclic quadrilateral | Tangential quadrilateral |
|---|---|
| Circumscribed circle | Inscribed circle |
| Perpendicular bisectors of the sides are concurrent at the circumcenter | Angle bisectors are concurrent at the incenter |
| The sums of the two pairs of opposite angles are equal | The sums of the two pairs of opposite sides are equal |
This duality is perhaps even more clear when comparing an isosceles trapezoid to a kite.
| Isosceles trapezoid | Kite |
|---|---|
| Two pairs of equal adjacent angles | Two pairs of equal adjacent sides |
| One pair of equal opposite sides | One pair of equal opposite angles |
| An axis of symmetry through one pair of opposite sides | An axis of symmetry through one pair of opposite angles |
| Circumscribed circle | Inscribed circle |
Read more about this topic: Dual Polygon