Triangle And Its Types Based On Size Of Sides And Angles

Definition

The chapter Polygon's Types And Classification Based On Sides defines a polygon as a closed curve, which is made up of only line segments.

Triangle is one type of polygon which has three sides or line segments. It is a polygon with the least number of sides, in other words, a polygon with less than three sides does not exist. A triangle is a closed figure which is formed by joining three line segments. It has 3 sides, 3 vertices and 3 angles. The triangle is denoted by Δ, a delta symbol.

The following figure shows a triangle whose name is ΔABC, where Δ is a symbol of triangle and ABC is the name of a triangle, which always includes three vertices of a triangle.

Example of a triangle ΔABC

We can use any three vertices in any order to represent a triangle. For example, ABC or BAC or CAB or ACB. Therefore, the triangle can also be written as ΔBAC or ΔCAB or ΔACB.

Number of sides

Triangle always has three sides. These sides are also called the line segments. So, in ΔABC, line segments AB, BC and CA are sides of the ΔABC. These three sides of a triangle are written as $\stackrel{━━}{\mathrm{AB}}$, $\stackrel{━━}{\mathrm{BC}}$, and $\stackrel{━━}{\mathrm{CA}}$.

Vertices

The vertex of a triangle is that point where any two sides of a triangle meet out or intersect. In the ΔABC in the above figure, sides AB and AC meet at point A. So, A is the vertex of ΔABC.

Similarly, sides BC and AB meet at point B. So B is a vertex of ΔABC. Also, sides AC and BC meet at point C. So C is a vertex of ΔABC. Therefore, A, B and C are the three vertices of ΔABC.

Angles

Angles in a triangle are formed at its vertex. It is a measurement of how slanted two lines are to each other. The angles are measured in degrees units. Let's understand angles in a triangle ΔABC from the above figure.

ΔABC has three vertices A, B and C. Therefore, we can say angles are formed at vertices A, B and C. Angles are written as ∠ABC, ∠BAC and ∠ACB or in a short form as ∠B, ∠A and ∠C respectively. In other words, we can say:

• ∠ABC or ∠B is formed at vertex B of ΔABC.
• ∠BAC or ∠A is formed at vertex A of ΔABC.
• ∠ACB or ∠C is formed at vertex C of ΔABC.

Types based on sides length

Triangle has many types depending upon the length of its sides.

Equilateral triangle

A triangle is said to be an equilateral triangle if all sides of a triangle are of equal length. ΔABC is an equilateral triangle because AB = BC = CA, where AB is length of side AB, BC is length of side BC and CA is the length of side CA.

Equilateral triangle ΔABC

Isosceles triangle

A triangle is said to be an Isosceles triangle if any two sides of the triangle are of equal length. ΔABC is an isosceles triangle because AB = AC.

Isosceles triangle ΔABC

Scalene triangle

A triangle is said to be a scalene triangle if all sides of the triangle are of unequal length. ΔABC is a scalene triangle because AB ≠ BC ≠ AC.

Scalene triangle ΔABC

Types based on size of angles

A triangle has many types depending upon the length of its angles.

Acute angled triangle

A triangle is said to be an acute angled triangle if each angle of a triangle is acute. An acute angle is that angle which is less than 90°.

So, the ΔABC in figure is an acute angled triangle because all angles are less than 90°. That is, ∠A, ∠B and ∠C are all less than 90°.

Acute angled triangle ΔABC

Right angled triangle

A triangle is said to be a right angle triangle if one of its angles is right angle. The right angle is that angle whose measure is 90°.

So, the ΔABC in figure is a right angled triangle because ∠C is equal to 90°.

Right angled triangle ΔABC

Obtuse angled triangle

A triangle is said to be an obtuse angled triangle if one of its angles is an obtuse angle. Obtuse angle is that angle which is greater than 90°.

So, the ΔABC in figure is an obtuse angled triangle because ∠C is greater than 90°.

Obtuse angled triangle ΔABC