A triangle is an important necessary measure in geometry with three sides, three heights and three angles . They occur in several shapes, each with plots that take part an important function in geometry. The sum of the inside angles of a triangle is equal to 180 degrees which is known as the angle sum property of a triangle. If PQR is a triangle, then it is presented as triangle PQR where P, Q and R are the heights of the triangle. A triangle is a two dimensional form that appears as three opposite points on an exotic flat surface. Various definitions of triangles, such as Pythagoras theorem and trigonometry, are based on the properties of the triangle.
Form of a triangle
Triangle is a sealed superficial form. It is a polygon made up of three sides. All sides of triangles are made in a horizontal pattern. The tip where two straight lines join is the crest. So, triangle has three heights. Each crest makes an angle.
Angles of a triangle
There are three angles in a triangle. These angles are created by the two sides of the triangle, which merges at a similar point known as the crest. The sum of three interior angles of a triangle is 180 degrees . If the side length of the triangle is increased outwards, an external angle is created. The sum of successive interior and exterior angles of triangle is supplementary.
Angle A , Angle B and Angle C are the interior angles of a triangle ABC. When the sides are increased in the outer direction , Angle D , Angle E and Angle F are formed externally which are sequential to Angle A, Angle B and Angle C individually.
Angle A+ Angle D= 180 degrees
Angle B + Angle E = 180 degrees
Angle C+ Angle F = 180 degrees
Angle( A+ B+C+ D+ E+F) = 180 degrees + 180 degrees + 180 degrees
By solving Angle Sum Properties
Angle ( A+ B+ C) = 180 degrees
So,
180 degrees + Angle ( D+ E+ F) = 180 degrees
Angle D + Angle E+ Angle F= 360 degrees
This provides a solution that the sum of the exterior angles of the triangle is 360 degrees.
Characteristics
Every figure has some characteristics which differentiate them from one another.
- A triangle has three sides and three angles
- The sum of the angles of triangle is equal to 180 degrees
- The outer angles of a triangle is equal to 360 degrees.
- The sum of uninterrupted inner and outer angle is supplementary
- The sum of the measures of any two sides of the triangle is more than the length of the third side. Similarly the difference between the measures of any sides of a triangle is below the length of the third side of the triangle.
TypesAccording to the length of the sides there are three types of triangle
a) Scalene triangle refers to the triangle whose three sides are not equal to each other
b) Isoscales triangle refers to the triangle whose only two sides are equal
c) Equilateral triangle refers to the triangle whose three sides are equal to each other. It is considered as the three sides polygon
According to the measurements of the angles in triangles there are three types of angles
a) Right angled triangle where one of the angle of triangle is equal to 90 degrees. Most right angled triangle is solved by doing Pythagoras theorum.
b) Acute Angled triangle where all the angles of triangles are between 0 to 90 degrees.
c) Obtuse Angle triangle where one of the angles of triangle is from 90 to 180 degree.
Mensuration of triangle
The perimeter of triangle is solved by adding the sides of a triangle and area is solved by 1/2 times of base multiplied by height .
