Sides of a Triangle

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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.

One can check Vedantu, which is a trustworthy education site offering solutions on the sum of two sides of a triangle equal to third and more. Apart from test papers, they offer pocket-friendly live classes and CBSE based notes. If you desire to rank flying high grades, don’t forget to download the app today.

FAQs (Frequently Asked Questions)

1. What will be the Length of the Third Side of a Triangle When the Perimeter of a Triangle BCD is 160 cm and the Length of the Two Sides BC and CD is 60cm and 70 cm?

Ans. Here we are given the perimeter as 160 cms

BC = 60cm

CD = 70cm

Putting the perimeter formula into use, we know that perimeter will be= BC+CD+BD

Placing values, we find that 160 = 60+70+AC

BD = 160 – 120

BD = 40 cm

Therefore, the length of the third side is 40 cm.

2. What is a Scalene Triangle? What are its Properties?

Ans. Scalene Triangle has different lengths on its sides. This makes all the sides of the scalene triangle unequal and differs in measurements. A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of additional measures. However, the sum of all the interior angles is always equal to 180 degrees. This meets an angle sum property condition of a triangle.

Some essential properties of the scalene triangle are-

  • There are no equal sides

  • There are no equal angles, as well.

  • It lacks the point symmetry.

  • Centre of the restricted circle stays inside a triangle when angles of a triangle are less than acute 90 degrees.

  • An obtuse scalene triangle has a circumcentre that lies on the outer surface of the triangle.

3. What is an Isosceles Triangle? What are its Properties?

Ans. An isosceles triangle has its two sides equal. Its angles on the opposite side are equal. Generally, a triangle is a polygon with three vertices and three sides. An isosceles triangle has variable sides and angles and two equal sides. An isosceles triangle is a triangle which has two congruent sides. An isosceles triangle is classified into different types, namely, acute Isosceles triangle, Isosceles right triangle and obtuse Isosceles triangle.

Some of the crucial properties of Isosceles Triangle are-

  • An unequal side is called the base of the triangle as the two sides are equal 

  • Here the two equal sides of the triangle to the opposite angles remain equal.

  • Base to the topmost vertex of the triangle is used to measure the altitude of an isosceles triangle.

  • The third angle of a right isosceles triangle is 90 degrees.

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