The Quadrilaterals part 1

Quadrilateral is a plane figure (polygon) with four sides and four vertices. It is also called tetragon and quadrangle. While in triangle, the sum of the interior angles is 180° ; for the quadrilaterals the sum of the interior angles is always equal to 360°

A + B + C + D = 360°

Classifications of Quadrilaterals

• Simple - sides of simple quadrilaterals do not cross each other
• Complex- sides of complex quadrilaterals cross each other

Classifications of Simple Quadrilaterals

• Convex- none of the sides pass through the quadrilateral when prolonged or extended
• Concave- prolongation of any one side will pass inside the quadrilateral

I. General Quadrilaterals

Note: This formulas are are applicable only to convex quadrilaterals.

Finding the Area of General Quadrilaterals given the four sides and sum of two opposite angles.

II. Cyclic Quadrilaterals

Acyclic quadrilateral is a quadrilateral in which all of its four vertices lie of a circle.

Finding the Area of Cyclic Quadrilaterals using Ptolemy's Theorem and Bramaguptha's Formula.

Ptolemy's Theorem

d₁ • d₂ = ac + bd

Note:

Opposite angles of cyclic quadrilateral are supplementary

A + C = 180°

B + D = 180°

III. Quadrilateral Circumscribing a Circle

Quadrilateral circumscribing a circle (also called tangential quadrilateral) is a quadrangle whose sides are tangent to a circle inside it.

Finding the Area of Quadrilaterals circumscribing a circle.

---