## Pre-Requisires

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A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. **(Scroll down to continue …)**

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**Curve:** Curve is a figure formed on a plane surface by joining a number of non linear points without lifting a pencil.

**Open Curve:** An open curve is a curve which does not end at the same starting point or which does not intersect itself.

**Closed Curve:** Closed curve is a curve which intersects itself or which starts and ends at the same point.

**Simple Closed Curve:** A simple closed curve is a closed curve that does not intersect itself.

**Polygon:** Polygon is a closed figure bounded by three or more line segments such that each line segment intersects the other two line segements at exactly two other points (vertices) as shown in the following figures.

Polygons are classified into two types on the basis of interior angles: as (i) Convex polygon (ii) Concave polygon

**(a) Convex Polygon: **In this case, each angle is either acute or obtuse (angle < 180 ^{o}) as shown in the following figures.

**Concave Polygon:** In this case, any one angle is reflex (angle > 180°) and one diagonal is outside the polygon as shown in the following figures.

On the basis of sides, there are two types of polygons :

(**a) Regular Polygon:** A convex polygon is called a regular polygon, if all its sides and angles are equal as shown in the following figures.

Each angle of a regular polygon of n-sides =

**Important results on polygon :**

For a regular polygon of n sides (n > 2).

**(b) Irregular Polygon:** A polygon in which all the sides are unequal as shown in the following figures,

**Triangle :**

A simple closed figure bounded by three line segments is called a triangle, it has three sides as AB, BC and AC; three vertices as A, B and C and three interior angles A, ZB and ZCand the sum of all angles is 180°.

i.e., <A + <B + <C = 180°

**Quadrilateral:** A simple closed figure bounded by four line segments is called a quadrilateral, it has four sides i.e.,

AB, BC, CD and AD and four vertices as A, B, Can d D and the sum of all angles of a quadrilateral is 360.

**Practical Geometry**

Five measurements can determine a quadrilateral uniquely.

A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.

A quadrilateral can be constructed uniquely if its two diagonals and three sides are

known.

A quadrilateral can be constructed uniquely if its two adjacent sides and three angles

are known.

A quadrilateral can be constructed uniquely if its three sides and two included angles

are given.

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