Triangle Definition

A triangle is a 3 -sided polygon with 3 edges and 3 vertices in geometry.  Interior angles sum equals 180 degrees is the feature of a triangle. The angle sum property of a triangle is the name for this property.

If EFG is a triangle, it is written as EFG, with E, F, and G as the triangle’s vertices. In Euclidean geometry, a triangle is a two-dimensional form made up of three non-collinear points in a single plane.

Triangle

A triangle is a closed 2-D polygon with 3 sides and a total angle of 180 degrees.

Types of triangle

There are various type of triangle are given below:

Types of triangle based on angle:-

The following are the different sorts of triangles based on  angles:

• Acute Triangle: An acute-angled triangle or acute triangle is formed when all of the angles of a triangle are acute, that is, they measure less than 90 degrees.
• Right angle triangle:-A right-angled triangle or right triangle is formed when one of the triangle’s angles is 90 degrees.
• Obtuse Triangle: An obtuse-angled triangle or obtuse triangle is one in which one of the triangle’s angles is more than 90 degrees.

Types of triangle on the basis of the sides and angles:-

The following are the different sorts of triangles, as well as their sides and angles:

• Equilateral or Equiangular Triangle: An equilateral or equiangular triangle is one in which all sides and angles are equal.
• Isosceles Right Triangle: An isosceles right triangle is a triangle with two equal sides and one 90° angle. Two sides and two acute angles are equivalent in an isosceles right triangle.
• Obtuse Isosceles Triangle: An obtuse isosceles triangle is defined as a triangle with two equal sides and one obtuse angle.
• Acute Isosceles Triangle: An acute isosceles triangle is one with all three angles being acute and two sides measuring the same length.
• A right scalene triangle is defined as a triangle in which any one of the angles is a right angle and all three sides are unequal.
• Obtuse Scalene Triangle: An obtuse scalene triangle is a triangle with an obtuse angle and sides of varying lengths.
• Acute Scalene Triangle: An acute scalene triangle is a triangle with three unequal sides and three acute angles.

Types of triangles based on sides :-

Triangles are categorized into the following types based on their side lengths:

• Equilateral Triangle: When all three sides of a triangle are the same length, it is called an equilateral triangle.
• Isosceles triangle: those triangles are called isosceles triangles which are formed when the two sides of a triangle are equal or congruent.
• Scalene triangle: A scalene triangle is one in which none of the triangle’s sides are equal.

Properties of triangle

Vertex:- A triangle’s vertex  is one of the triangle’s corners. There are 3  vertices in a triangle.

Base:-A triangle’s base might be any of the three sides, but it’s usually the one at the bottom.  When computing the area of a triangle, this is commonly used as a reference side. The base of an isosceles triangle is commonly assumed to be the uneven side.

Altitude :-The perpendicular from the base to the opposite vertex is the height of a triangle. The three altitudes meet at a single location known as the triangle’s orthocenter. 

Median:-The median of a triangle is a line drawn from one vertex to the opposing side’s midway. The three medians meet at a single point known as the triangle’s centroid. 

Area :-commonly we find area of triangle find by the formula :

                Triangle ares’s  = ½× base × height.

Perimeter:-The circumference of the triangle. The perimeter of a triangle is equal to the sum of its three sides.Let us suppose a triangle ABC . Sides of the triangle are AB,BC and AC.

 So, the perimeter of the triangle is the sum of these given sides of the triangle . i.e. perimeter of triangle = AB +BC+ AC.

The three angles on the inside of the triangle at each vertex are known as interior angles.

Exterior angles are the angles formed by a triangle’s side and a neighboring side’s extension.

Point to Remember: 

• Each of the three internal angles in an equilateral triangle is 60 degrees
• The sum of all angles of the triangle’s three interior angles is always 180°
• There are two sharp angles in every triangle
• A triangle is called equilateral or equiangular when all of its sides and angles are equal

Conclusion

A triangle is a 3 -sided polygon with 3 edges and 3 vertices in geometry.  Interior angles sum equals 180 degrees is the most significant feature of a triangle. The angle sum property of the triangle is the name for this property.

Acute triangle, obtuse triangle, right triangle, equilateral triangle, isosceles triangle, and scalene triangle are the  types of triangles. Triangle are classified on the 3 basis  that are side ,angle and side & Angle