A triangle is a polygon with three sides and three angles. It is one of the simplest and most fundamental shapes in geometry. A triangle has these key Properties:
- Sides: A triangle has three sides, which can have different lengths.
- Angles: A triangle has three interior angles, and the sum of these angles is always 180°.
- Vertices: A triangle has three vertices (corner points), where two sides meet.
In the figure above, check out triangle ABC. It has vertices A, B, and C, and sides AB, AC, and BC.
What are the Different Types of Triangles?
Triangles can be classified based on sides and based on angles. Classification of triangles is done based on the following characteristics:
- Types of Triangles Based on Sides
- Types of Triangles Based on Angles
Types of Triangles based on sides
Based on sides, There are 3 types of triangles.
- Equilateral Triangle
- Isosceles Triangle
- Scalene Triangle
Types of Triangles based on SidesEquilateral Triangles: Equilateral triangles are triangles where all sides and angles are equal. Because all angles are the same, each angle in an equilateral triangle is 60°. Another name for an equilateral triangle is an equiangular triangle. Here length of the sides and angles is equal to each other.
Isosceles Triangles: An isosceles triangle is a triangle where two sides are equal, and the third side is not equal to the other two. The angles opposite to the equal sides of this triangle are also equal.
Scalene Triangles: A scalene triangle is one where none of the sides are equal, and none of the angles are equal either. However, the general properties of triangles still apply to scalene triangles. Hence, the sum of all the interior angles is always equal to 180°
Types of Triangles based on angles
Based on the interior angles of a triangle, we can classify the triangle into three types:
- Acute Angled Triangle
- Right Angled Triangle
- Obtuse Angles Triangle
Acute Angled Triangle: An Acute angled Triangle is one where all the interior angles of the Triangle are less than 90°. For Instance, an Equilateral Triangle is an acute-angled triangle (all angles are less than 90°).
Right Angled Triangle: A Right Angled Triangle is one where one of the angles is always equal to 90°. Pythagoras' Theorem applies to right-angled triangles. It says that the square of the hypotenuse (the longest side) equals the sum of the squares of the base and perpendicular.
Obtuse Angled Triangle: In an obtuse-angled triangle, one angle measures more than 90°. Here, one of the three angles is greater than 90°, making the other two angles less than 90°.
Classification Based on the Sides and Angles of Triangle
There are various other types of triangles based on both angles and sides of the triangle, some of these types are:
- Isosceles Right Triangle
- Obtuse Isosceles Triangle
- Acute Isosceles Triangle
- Right Scalene Triangle
- Obtuse Scalene Triangle
- Acute Scalene Triangle
For Isosceles Triangle:
Isosceles Right Triangle: An isosceles right triangle, also called a right isosceles triangle, has two main characteristics. First, it possesses two sides of equal length, often referred to as the legs. Second, it contains one angle measuring exactly 90 degrees, known as the right angle.
For example, look at triangle ABC. Sides AB and BC both measure 8 centimeters (AB = BC = 8cm), and angle B is a right angle (∠B = 90°). It's an Isosceles Right Triangle.
Obtuse Isosceles Triangle: An Obtuse Isosceles Triangle is a triangle with two sides equal and one interior angle measuring more than 90°.
For Example, in triangle PQR, sides PQ = PR = 10 cm, and ∠P = 110°, it's an Obtuse Isosceles Triangle.
Acute Isosceles Triangle: An Acute Isosceles Triangle is a triangle with two equal sides, and all interior angles measuring less than 90°.
For Example, in triangle LMN, sides LM = LN = 8 cm, and ∠M = ∠N = 70°, it's an Acute Isosceles Triangle.
For Scalene Triangle:
Right Scalene Triangle: A Right triangle is a triangle with all sides of different lengths and one interior angle to be 90°.
For example, in triangle ABC, sides AC = 6 cm, BC = 8 cm and AB = 10 cm. Plus, angle C measures 90 degrees, making it a perfect example of a Right Scalene Triangle.
Obtuse Scalene Triangle: An Obtuse Scalene Triangle is a triangle with all sides of different lengths and one obtuse angle.
For example, in triangle DEF where all three sides are different lengths. On top of that, one of the angles inside, ∠F, opens extra wide at 135 degrees, more than a right angle! That's what makes DEF an Obtuse Scalene Triangle.
Acute Scalene Triangle: An Acute Scalene Triangle is a triangle with all angles less than a right angle and all sides of different lengths.
For Example: in triangle GHI, where each side is of different length: GH = 5 cm, HI = 7 cm and IG = 9 cm. And all three angles are sharp, none wider than a right angle with ∠I = 60 degrees. That makes GHI an Acute Scalene Triangle.
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