Are you looking for some quick all over the Web but can't find any? Well, bring your search to an end with this bit of article. It compiles some vital concepts and shortcut tricks.

Let’s begin.

**Diagonals Of a Polygon**

One of the most common questions in any involves polygons, where teachers might ask students to find how many diagonals a specific convex polygon has. For example, Pentagon, Hexagon, Rectangles etc., are all convex polygons as it is impossible to draw an external diagonal in case of any of these shapes.

Let us consider a polygon of ** n **sides and, thus,

**vertices.**

*n*Each of the

vertices can be connected to*n*other vertices with the diagonals. Moreover, a vertex can be connected to any other vertex other than itself and the ones on its sides. Thus, there are*(n-3)*lines that can be drawn as diagonals.*[n* (n-3)]*

The actual number is

as in the above point, we considered drawing from both endpoints of a diagonal.*half of [n**n-3)]*

\

So, the formula for the number of diagonals in an n-sided polygon is [

.*n*(n-3)/2]*

**Triangles And Their Features**

Take note of the following points for your **. **They can **help **you solve tricky sums of triangles with ease.

The line which divides any angle into two equal parts is the angle bisector.

** **

The meeting point of all angle bisectors is called the in-centre. The in-centre is the centre of the in-circle of a triangle.

** **

The in-centre

is equidistant from all sides of a triangle.*I*

** **

If

is the in-centre of the triangle above, then*I**angleBIC=90 deg + (angle A/2).*

** **

The semi-parameter of a trian