Triangles in Geometry
Education

Facts about Triangles in Geometry

Everything we observe in the world has a shape to it. In the items we see around us, we can find different primary forms such as the two-dimensional triangle, square, and rectangle and the three-dimensional rectangular prism, cone, sphere and cylinder. Credit cards, finger rings, photo frames, buildings, windows, flower pots, toy railways, and balloons are all examples of geometric shapes. As a result, a shape can be defined as an object’s shape, outline, outer boundary, or outer surface. Here, let us discuss everything about triangles in detail.

What are Triangles?

Triangles are three-sided polygons with three angles that can be made by connecting any three points in a plane. Triangles are one of the first geometric shapes to be studied. Triangles are particularly useful because arbitrary polygons (with 4, 5, or n-sides) can be broken into triangles. Understanding the fundamental properties of triangles allows for a more in-depth examination of these larger polygons. The triangle is the only rigid polygon built out of straight-line segments, which means that the measurements match a unique triangle provided the three side lengths are given. 

Triangle Properties

The essential triangle properties are as follows:

  • Three sides, three angles, and three vertices make up a triangle.
  • The total of a triangle’s interior angles is always 180 degrees. This is termed the angle sum property of a triangle.
  • The length of any two triangle sides added together is more than the length of the third side.
  • The greatest side of a triangle is the side opposite the largest angle.
  • The sum of the triangle’s interior opposite angles equals any of its outer angles. It is referred to as a triangle’s exterior angle property.

Triangle Types

Triangles are classified into six types based on their side length and interior angles. Based on the side lengths of a triangle, the triangle is classified as a scalene, isosceles and equilateral triangle.

Scalene Triangle – A scalene triangle is one in which three sides have a different side length. As a result, the three angles are distinct from one another.

Isosceles Triangle – Two sides of an isosceles triangle are of equal length. The two angles that are opposite the two equal sides are also equal.

Equilateral Triangle – All three sides of an equilateral triangle are the same length. As a result, all internal angles are of the same degree, i.e. each angle is 60 degrees.

The triangle is classified as an acute, obtuse, and right angle triangle based on the measurement of angles. Now, let us discuss these three types of triangles in brief.

Acute Triangle – In an acute triangle, all angles are less than 90 degrees.

Obtuse Triangle – An obtuse triangle has one angle more than 90 degrees.

Right Triangle – In a right triangle, one of the angles is exactly 90 degrees, called a right angle.

Area of Triangle

The area of a triangle is the space occupied by a triangle in the two-dimensional space. If “b” is the base and “h” is the triangle’s height, then the area of a triangle equals half of the base times height.

Area of a triangle = (½) × Base × Height Square units

Perimeter of Triangle

The perimeter of a triangle is the total length of the triangle’s outer boundary. The perimeter is measured in the same way as the triangle’s sides are measured. Or, to put it another way, the triangle’s perimeter is equal to the total of its three sides.

The perimeter of a triangle = Sum of all Sides (units)

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