[Maths Class Notes] on Sides of a Triangle Pdf for Exam

A triangle is a form of a polygon with three sides or edges and vertices. A polygon is a two dimensional, closed, and flat with multiple corners. Sides of a triangle form the basic shape in geometry. Ideally, A, B, and C are used to denote three sides. 

The sum of three angles forms the interior angles in this shape which is 180 degree. A line segment that joins a triangle’s vertex to the centre point in opposite sides is called a median. The end in the interaction of medians is called the centroid, while the length in the right angles from vertex is called altitude. 

According to Euclidean geometry, a non-collinear having three points’ forms an inimitable plane which has a distinctive plane. It is, therefore, stays in a single plane. However, this statement isn’t applicable in higher-dimensional Euclidean spaces. 

In this segment, students will learn ways to use triangle formula sides and their limitations in an equation. 

How to Find the Side of a Triangle?

To find the sides in this shape, one can use various methods like Sine and Cosine rule, Pythagoras theorem and a triangle’s angle sum property. Students need to know how to apply these methods, which is based on the parameters and conditions provided.

Ideally, there are three types of this shape based on the length in the sides of a triangle. They are- 

• Isosceles Triangle

• Scalene Triangle

• Equilateral Triangle

To find a side of a triangle, we can use Pythagoras theorem. Here is an explanation on how to apply this formula. 

How to Find the Third Side of a Triangle Using Pythagoras Theorem?

In a right-angled triangle, if perpendicular and base of hypotenuse are its sides, then this theorem says that the square hypotenuse side will be similar to base square and perpendicular square’s sum.

We can use formula Hypotenuse² = Base² + Perpendicular²

Therefore, by knowing two sides in this shape, one can easily find the third side of the triangle. Even the angle sum property and the total sum interior angles will always be 180 degrees.

What is the Third Side of a Triangle When one Uses Perimeter Formula?

The perimeter of this shape is always equal to the sum of its sides. By using this, we can find the total length. One can consider a triangle with sides B, C, D then according to this theorem the formula will be –

Perimeter will be BCD = BC + BD + CD

If two sides of this shape and its perimeter is given, then finding the length of the third side of triangle will be hassle-free.

If an equation gives only an angle of a side length, then one can use the rule trigonometry ratio to find other sides. In a triangle with θ angle between two sides then the sine, cos and tan ratio will be-

Cos θ = Length of bottom side divided by Length of Hypotenuse side

Sine θ = Length of contrary side divided by Length of Hypotenuse side

Tan θ = Length of a right-angle side divided by Length of Base side

Apart from practising equations based on sides of a triangle, a student needs proper guidance on related theorems. For strengthening base on mathematical equations, they require top-notch study materials and test papers.

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