Triangle – Properties of Plane Shapes

A triangle is a three-dimensional plane figure with three angles. In a triangle, the three interior angles always add up to 180°.

Properties of a Triangle:

a. A triangle has three sides, three angles, and three vertices.

b. A sum of the angles in a triangle = 180°

∠A + ∠B + ∠C = 180°

c. The height “h” of a triangle is the length of a line segment that connects the base “b” to the opposite vertex and makes a 90° angle with the base.

The base of a triangle refers to any side of a triangle, which is perpendicular (makes a 90° angle) to its height or altitude.

d. Any side of a triangle is less than the sum of two other sides and greater than their difference.

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

Types of Triangles:

Triangles can be broadly classified into two types, which are:

• Triangles based on the lengths of their sides
• Triangles based on their interior angles

In this topic, we will be discussing these two classifications of triangles along with their properties.

Classification of Triangles:

S/n	Based on their Sides	Based on their Angles
1.	Scalene Triangle	Acute Triangle
2.	Isosceles Triangle	Obtuse Triangle
3.	Equilateral Triangle	Right Triangle

Types of Triangles Based on Sides:

i. Scalene Triangle:

A scalene triangle has no equal sides and no angles equal.

ii. Isosceles Triangle:

An isosceles triangle has two adjacent sides equal and two angles equal.

iii. Equilateral Triangle:

An equilateral triangle has all its sides equal and all its angles equal. Each angle is 60°.

Types of Triangles Based on Angles:

i. Acute Triangle:

An acute-angled triangle has each of its angles less than 90° i.e. each angle is acute.

Note: A scalene may not always be an acute triangle. It can be a right-angled triangle with angles of 90°, 40°, and 50°. A scalene triangle can also be an obtuse triangle with angles 20°, 50°, and 110°. Three interior angles of an acute triangle must be less than 90°.

ii. Obtuse Triangle:

An obtuse-angled triangle has one of its angles greater than 90°.

iii. Right-angled Triangle:

• A right-angled triangle has one of its angles equal to 90°.

• The opposite of the right angle is the longest side and it’s often called the hypotenuse.

Also, note that a right-angled triangle must have two acute angles. As a right triangle has one angle equal to 90°, this means the sum of the remaining two angles must be 180° – 90° = 90°. So the remaining two angles must be acute and can be 60° + 30°, or 55° + 35°, etc.