A triangle is a polygon with three sides (edges), three vertices (corners), and three angles.
- It is the simplest polygon in geometry, and the sum of its interior angles is always 180°.
- It is formed by three line segments (edges) that intersect at three vertices, creating a two-dimensional region.
The triangle, △PQR, given in the image below, shows the vertices, sides, and interior angles of a triangle.
- The three angles of the triangle are ∠PQR, ∠QRP, and ∠RPQ.
- The three sides of the triangle are side PR, side PQ, and side RQ.
- There are three vertices of a triangle, which are P, Q, and R.
Area and Perimeter
The area and perimeter are two important measurements used to describe a triangle.
Perimeter: The perimeter of a triangle is the total length of all its sides. It can be calculated by adding the lengths of the three sides of the triangle.
Area: The area of a triangle is the total area covered by the triangle boundary. It is equal to half the product of its base and height. It is measured in square units.
Types of Triangles
Triangles can be classified based on their sides and angles:
- Equilateral Triangle: All three sides are equal, and all three interior angles are equal.
- Isosceles Triangle: Two sides are equal in length, and the angles opposite these sides are also identical. The area can be calculated using the standard triangle area formula.
- Scalene Triangle: All sides are of different lengths, and all interior angles are unequal, making the triangle irregular in shape.
- Acute-Angled Triangle: All three interior angles are greater than 0° and less than 90°, so each angle is acute.
- Obtuse-Angled Triangle: One interior angle is greater than 90°. Since the sum of the interior angles is 180°, the other two angles are less than 90°.
- Right-Angled Triangle: One interior angle is exactly 90°. The side opposite the 90° angle is the longest and is called the hypotenuse.