How Many Independent Components are Required to Construct a Triangle

Introduction.

We have heard about many shapes or polygons. But constructing these shapes has a definite set of instructions or ways, which results in the formation of a perfect shape. For constructing a triangle, we need three independent components, drawn distinctly. If only two lines are used, it doesn't even make a closed polygon, and if we use four, five, and six lines or components, we get a quadrilateral, pentagon, and hexagon respectively. The minimum number of lines to create a closed polygon is three, and it forms a triangle!

A triangle has six components - 3 sides and 3 angles, where the angles make up a total of 180°. But we will always need any three components to create a triangle.

How to Construct a Unique Triangle?

For constructing a unique triangle, you will need to know any one of the following specifications :

1. Length of three sides. (Side Side Side - SSS Theorem). In this theorem, to draw a triangle, the sum of the lengths of any two sides must be greater than the third side. Otherwise, you won't be able to draw a perfect triangle!

2. Length of two sides and the angle included in between them. (Side Angle Side -SAS Theorem )

3. Length of one side and the angle situated at both ends of the side. (Angle Side Angle - ASA Theorem ).

In the above picture, A and B are the angles, and AB is the side in between them.

The above rules are also used to draw congruent triangles, that is equal triangles. And also note that if three angles are given, you will not be able to construct a specific, unique triangle. If you don't mind the measurements and want to draw a triangle randomly, none of these theorems is needed. But use these to draw an exactly oriented triangle!

Think About This

If you are given the measurement of two sides and an angle that is not situated between them, will you be able to draw a specific triangle? The answer is no. So now you may have understood that any random three measurements are not useful in constructing a triangle, but you need them in a very specific combination.

Different Types of a Triangle

Now, let's look at the various types of triangles and their construction.

• Equilateral triangle: It is a kind of triangle with three equal sides and three equal angles. Now the most important thing is that the angle you need to draw an equilateral triangle will always be 60°.

• Isosceles triangle: In this type of triangle, any two sides and the angle opposite to these respective sides will always be equal.

• Right-angled triangle: It is in the name itself - the triangle has a right angle or 90° angle. To construct such a triangle, you will need the measurements of one side, a hypotenuse, and a 90° angle.

Conclusion :

To draw an accurate triangle, you require a minimum of three independent components. It can be the length of the sides, or it may be the angles but atleast one side. These are required to draw a much more proper triangle rather than drawing a random one.