What Are the Sides of a Triangle Definition Properties and Solved Examples
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 on Sides of a Triangle Explained with Properties and Types
1. What are the sides of a triangle?
The sides of a triangle are the three line segments that join three non-collinear points to form a closed shape. Each side connects two vertices, and together they determine the triangle’s size and shape. In triangle ABC, the sides are:
- Side AB
- Side BC
- Side CA
2. How many sides does a triangle have?
A triangle has exactly 3 sides. These three sides connect three vertices and form a closed polygon. Because it has three sides and three angles, a triangle is also called a three-sided polygon. No triangle can have more or fewer than three sides.
3. What is the triangle inequality theorem for sides of a triangle?
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side. If the sides are a, b, and c, then:
- a + b > c
- b + c > a
- c + a > b
4. How do you find the perimeter using the sides of a triangle?
The perimeter of a triangle is the sum of its three side lengths. The formula is:
Perimeter = a + b + c
- If a = 5 cm, b = 7 cm, and c = 9 cm
- Perimeter = 5 + 7 + 9 = 21 cm
5. How are triangles classified based on their sides?
Triangles are classified by their sides into equilateral, isosceles, and scalene triangles. The classification depends on side lengths:
- Equilateral triangle: All three sides are equal.
- Isosceles triangle: Two sides are equal.
- Scalene triangle: All three sides are different.
6. What is the longest side of a right triangle called?
The longest side of a right triangle is called the hypotenuse. It is the side opposite the 90° angle. According to the Pythagoras theorem:
Hypotenuse² = Base² + Perpendicular²
For example, if the legs are 6 and 8, then:
- Hypotenuse² = 6² + 8² = 36 + 64 = 100
- Hypotenuse = 10
7. How do you find a missing side of a right triangle?
A missing side of a right triangle can be found using the Pythagoras theorem: a² + b² = c². Follow these steps:
- Identify the hypotenuse (longest side).
- Substitute known values into the formula.
- Solve for the unknown side.
- 5² + b² = 13²
- 25 + b² = 169
- b² = 144
- b = 12
8. Can three given side lengths always form a triangle?
Three given side lengths can form a triangle only if they satisfy the triangle inequality condition. The sum of any two sides must be greater than the third side. For example:
- Sides 4, 5, and 6 form a triangle because 4 + 5 > 6.
- Sides 2, 3, and 6 do not form a triangle because 2 + 3 < 6.
9. What is the relationship between the sides and angles of a triangle?
In a triangle, the larger side is opposite the larger angle, and the smaller side is opposite the smaller angle. This means:
- If one angle is the largest, its opposite side is also the longest.
- If two sides are equal, their opposite angles are equal.
10. What is the formula to find the area using the sides of a triangle?
The area of a triangle using its three sides can be found using Heron’s formula. First calculate the semi-perimeter:
s = (a + b + c) / 2
Then apply:
Area = √[s(s − a)(s − b)(s − c)]
Example: If sides are 3, 4, and 5,
- s = (3 + 4 + 5)/2 = 6
- Area = √[6(6−3)(6−4)(6−5)] = √[6 × 3 × 2 × 1] = √36 = 6 square units
