The triangle is a closed polygon that has 3 angles, 3 sides, and also three vertices. Based upon the size of sides and also meacertain of angles, the triangles are classified into various types of triangles.Properties of a triangle assist us to determine a triangle from a offered set of figures easily and also conveniently.

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In the start, we begin from knowledge the form of triangles, their forms, and also properties, theorems based upon them such as Pythagoras theorem, and so on Let us learn right here some fundamental properties of triangles.

1.Triangles: Group by Type
2.Triangle Properties
3.Solved Examples
4.Practice Questions

Triangles: Category by Type

Triangles can be classified right into two wide categories based upon their angles and sides. Based on angles, tright here are 3 types of triangles, and also based upon sides, tbelow are 3 forms of triangles.


Triangle Properties

Properties of a triangle aid us to determine relationships between various sides and also angles of a triangle. A few of the important properties of a triangle are listed listed below.

Property 1 - Angle Sum Property

As per the angle amount residential property, the sum of the 3 interior angles of a triangle is always 180°.


In the provided triangle, angle P + angle Q + angle R = 180°

Property 2 - Triangle Inequality Property

As per the triangle inetop quality residential or commercial property, the sum of the size of the two sides of a triangle is greater than the third side.


In △ ABC and also △ PQRa + b > c ( 6 + 4 > 3)c + a > b (3 + 4 > 6)c+ b > a ( 6 + 3 > 4)

Property 3 - Pythagorean Theorem

As per the Pythagorean theorem, in a appropriate triangle, the square of the hypotenusage equals the amount of the squares of the various other two sides. Mathematically, it deserve to be expressed as Hypotenuse² = Base² + Altitude².


Property 4 - Side oppowebsite the higher angle is the longest side

In order to understand also the side oppowebsite the greater angle is the longest side home, let's take the below-given triangle right into consideration.


In this triangle, angle B is the biggest angle. Thus, the side AC is the longest side.

Property 5 - Exterior Angle Property

As per the exterior angle home, the exterior angle of a triangle is always equal to the sum of the interior oppowebsite angles.


In the provided triangle, Exterior angle E1 = angle PQR + angle QRPTright here are 3 exterior angles in a triangle and also all these exterior angles add approximately 360° for any kind of polygon.

Property 6 - Congruence Property

As per the Congruence Property, 2 triangles are sassist to be congruent if all their equivalent sides and angles are equal.


angle XYZ = angle DEFangle YXZ = angle EDFangle YZX = angle EFDXY = DEXZ = DFYZ = EF

The fundamental triangle properties such as the location and also perimeter of a triangle are given below.

Area of a triangle: The complete amount of room inside the triangle is referred to as the area of a triangle. The location is measured in square systems.The general formula for calculating the area of a triangle is Area (A) = (1/2) × Base × HeightPerimeter: The perimeter of a triangle = sum of all its three sides

Heron's formula: Heron’s formula is supplied to calculate the location of a triangle if the lengths of all the sides are recognized and also the height of the triangle is not known. First, we should calculate the semi-perimeter(s). For a triangle through sides p, q, and also r, s = (p+q+r)/2, the location is provided by; A = (sqrtS(S-P)(S-Q)(S-R))

Properties of a Triangle Related Topics

Check out these amazing short articles to recognize even more around properties of a triangle and also its related topics.

Important Notes

The triangle is a closed polygon that has actually three angles, 3 sides, and also three vertices.Sides and also angles are incredibly crucial facets of a triangle.We deserve to classify assorted types of triangles in math by combining sides and angles.The basic formula for calculating the area of a triangle is Area (A) = (1/2) × Base × HeightThe perimeter of a triangle is equal to the amount of all three sides of the triangle.

Example 3:A triangle has a measurement of 3 cm, 4 cm, and 5 cm, wbelow the base is 4 cm and also the altitude of the triangle is 3.2 cm. Calculatethe location and perimeter of the triangle.


Sides of the triangleare: x= 3 cm, y= 4 cm and also z= 5 cmAltitude= 3.2 cm

Using the location of the triangle formula, we know, Area = 1/2 × base × heightA = (1/2) × 4 × 3.2A = 6.4

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The perimeter of the triangle is offered by P = x+ y+ zP = 3 + 4 + 5P = 12 cmBecause of this, the location and perimeter of the given triangle are 6.4 cm2 and 12 cm respectively.