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.