Advanced geometry is the topic that is again divided into the sub categories like polygons, transformations,

**Polygons**

A polygon is a closed structure which is made up of straight lines and anglesin between them. They are 2-dimensional shapes; and the points where two edges meet are the polygon's vertices or corners.

Area of a regular polygon = (1/2) N sin (360°/N) S2

Sum of the interior angles of a polygon = (N - 2) x 180°

The number of diagonals in a polygon = 1/2 N (N-3)

S = length from center to a corner

N= Number of sides

The polygons are represented as shown below:

## Transformations

A transformation could be any function mapping a set X on to another set or on to itself. Generally a set X has some additional algebraic or geometric structure and the term transformation refers to a function from X to itself which preserves this structure. Transformations can be carried out in two ways as said below like linear transformations and geometric transformations rotations, reflections and translations. These can be carried out in coordinate plane, particularly in dimensions 2 and 3. They are also operations that can be performed using linear algebra, and described explicitly using matrices.

## Right Triangle

Right angled triangle takes an important role in mathematics such that it is used in trigonometry where the complete basics are related to right triangle, and in geometry help it plays an important role such that many complex problems can be solved using this right triangle. Pythagoras theorem is the most important theorem in mathematics this is derived from the right triangle.

**Pythagoras theorem**

AB^{2} + BC^{2 }= AC^{2}

Analytical geometryis also known as coordinate geometry; it only deals with the coordinate plane. Analytical geometry is used in case of graphing, developing 2 dimensional and 3 dimensional plotting and it also deals with straight lines, squares, polygons, parabolas etc. The 2D coordinate axis contains two axis x and y axis and where as 3D coordinate axis has got 3 axis i.e. x, y ,and z axis.

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## Circle Definition

A circle is a simple shape of coordinate geometry consisting of all points in a plane which are equidistant from a given point called the center. The common distance of the points of a circle from its center is called its radius.