Triangle Construction

We all are already aware about the concept of Triangle. 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. But before we move to that, in this section, we bring to you all the properties of triangles that you need to keep in mind before moving over to 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.

Internal Angle Property

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

External Angle Property

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

Triangle Property

  • 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.

Pythagoras Theorem

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

SSS Criteria

All three sides are given (SSS)

2. Construction Triangle given Perimeter and two angles

Perimeter and Two sides given

Perimeter of Triangle and two base angle

3. Constructing Triangles using ASA criteria

ASA criteria

Two angles and side between them (ASA)

4. Constructing Triangles using SAS criteria

SAS criteria

Two sides and angle between them (SAS)

5. Constructing Triangles using RHS criteria

RHS criteria

Right angled Triangle given Hypotenuse and a Side.

Learn more about Congruence of Triangle, constructing triangles with BYJU’S.

Practise This Question

The lines shown below never meet at any point. So, these lines are not parallel. Say true or false.