# Triangle Construction

A Triangle is a three sided Polygon made up of Three sides having three angles. It is to be noted that in the construction of triangle the three sides and angle may or may not be equal in dimensions.

Practical geometry, which deals with the construction of different geometrical figures, is an important branch of Geometry. Using a set of geometrical tools such as rulers, compasses and protractors, different shapes like squares, triangles, circles, hexagons, etc. can be constructed. The only condition is that you should be aware of the properties of these figures that set them apart from one another. You are already aware of the construction of lines, angles, bisectors, etc. This knowledge is extended for triangle construction.

## Properties of Triangles:

Different triangles have different properties. Some of the common properties of all triangles are listed below.

- The sum of the three interior angles of a triangle is 180 degrees.

- The measure of the exterior angle is equal to the sum of the opposite interior angles.

- The sum of lengths of two sides of a triangle is always greater than the length of the third side.

- Pythagoras Theorem: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the length of the other two sides.

## Criteria for Construction of Triangle:

For the construction of Triangle all its dimension and angles need not be required.

Any of the following set of measurement are required to construct a triangle:

1. Construction for SSS criteria

**All three sides are given (SSS) **

2. Construction Triangle given Perimeter and two angles

**Perimeter of Triangle and two base angle**

3. Constructing Triangles using ASA criteria

**Two angles and side between them (ASA)**

4. Constructing Triangles using SAS criteria

**Two sides and angle between them (SAS)**

5. Constructing Triangles using RHS criteria

Right angled Triangle given Hypotenuse and a Side.