Triangle and its types

 

DEFINITION OF A TRIANGLE

A triangle is a two-dimensional closed polygon having three sides and the sum of all three angles as 180 degrees.

TYPES OF TRIANGLES

For the classification of triangles according to their angles, we measure each of its interior angles and the triangles can be classified by angles, as follows:

• Acute Angled Triangle: An acute triangle has all interior angles acute (less than 90°)
• Right Angled Triangle: A right triangle has one right angle (equal to 90°)
• Obtuse Angled Triangle:  An obtuse triangle has one obtuse angle (greater than 90°)

Classification according to sides

For classification of the triangles according to their sides, we measure the length of each side of the triangle and the triangles can be classified by their sides, as follows:

• Equilateral Triangle: A triangle having all three sides of the same length is known as an equilateral triangle. Since all three sides are of the same length, all the three angles will also be equal. All interior angles of an equilateral triangle are equal to 60°

• Isosceles Triangle: A triangle having two sides of the same length and the third side of a different length is an isosceles triangle.

The angles opposite to the equal sides are equal.

• Scalene Triangle: A triangle having all three sides of different lengths is a scalene triangle.

Due to the three sides having different lengths, the three angles will also be of different measurements.

Classification according to angles and sides

For the classification of triangles according to both angles and sides, we measure the interior angles and length of the sides of the triangle. The triangles can be classified as follows:

Special cases of right-angled triangles

45-45-90 triangle

In such a triangle,

• Two angles measure 45°, and the third angle is a right angle.
• The sides of this triangle will be in the ratio – 1: 1: √2 respectively.
• This is also called an isosceles right-angled triangle since two angles are equal

30-60-90 triangle

In such a triangle,

• One angle = 90°
• The angles of this triangle are in the ratio – 1: 2: 3
• The sides opposite to these angles will be in the ratio – 1: √3: 2 respectively
• It is classified as a scalene right-angled triangle since all three angles are different.

Properties of triangle

• Angle sum property

The sum of all internal angles of a triangle is always equal to 180°. This property is called the angle sum property of a triangle.

The sum of all exterior angles of any triangle is equal to 360°

Example:

Note:- The sum of the length of any two sides of a triangle is greater than the length of the third side.

The side opposite to the largest angle of a triangle is the largest side.

Exterior Angle Property

Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This property is called the exterior angle property of a triangle.