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TYPES OF TRIANGLES

__TYPES OF TRIANGLES -__

**Triangles are a fundamental geometric shape with three sides and three angles. They are classified based on the size of their angles and the length of their sides. Here are some key types of triangles:-**

** 1. Based on Angles:-**

** a) Acute Triangle:- All angles are less than 90 degrees.**

** b) Obtuse Triangle:- One angle is greater than 90 degrees.**

** c) Right Triangle:- One angle is exactly 90 degrees.**

** 2. Based on Sides:-**

** a) Equilateral Triangle:- All three sides are of equal length, and all angles are equal (60 degrees each in the case of an equilateral triangle).**

** b) Isosceles Triangle:- Two sides are of equal length.**

** c) Scalene Triangle:- All three sides have different lengths.**

** 3. Special Triangles:-**

** a) 45-45-90 Triangle:- An isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The sides are typically in the ratio 1:1:√2.**

** b) 30-60-90 Triangle:- A right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are typically in the ratio 1:√3:2.**

** 4. Centroid, Incenter, Circumcenter, and Orthocenter:-**

** a) Centroid:- The point of concurrency of the medians of a triangle.**

** b) Incenter:- The point of concurrency of the angle bisectors of a triangle.**

** c) Circumcenter:- The point of concurrency of the perpendicular bisectors of the sides of a triangle.**

** d) Orthocenter:- The point of concurrency of the altitudes of a triangle.**

** 5. Pythagorean Theorem:- In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.**

**Triangles have applications in various fields, including geometry, physics, engineering, and computer graphics. They are fundamental to many mathematical principles and have practical uses in solving real-world problems.**