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PROPERTIES OF TRIANGLE

__PROPERTIES OF TRIANGLE -__

**Triangles are fundamental geometric shapes with several properties that mathematicians and scientists study. Here are some key properties of triangles:**

__Three Sides:-__A triangle is a polygon with three sides. Each side is a line segment that connects two vertices.__Three Angles:-__A triangle has three internal angles formed where its sides intersect. The sum of the interior angles of a triangle is always 180∘ (or π radians).__Types Based on Sides:-____Equilateral Triangle__:- All three sides are of equal length, and all three angles are equal, each measuring 60∘.__Isosceles Triangle__:- Two sides are of equal length.__Scalene Triangle__:- No sides are of equal length.__Types Based on Angles:-____Acute Triangle__:- All interior angles are less than 90∘.__Right Triangle__:- One interior angle is 90∘. The side opposite the right angle is the hypotenuse.__Obtuse Triangle__:- One interior angle is greater than 90∘.__Triangle Inequality Theorem:-__The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Mathematically, if a, b, and c are the lengths of the sides of a triangle, then:- (a + b > c), (a + c > b), (b + c > a)__Altitudes, Medians, and Angle Bisectors:-____Altitudes__:- Lines drawn from each vertex perpendicular to the opposite side.__Medians__:- Lines drawn from each vertex to the midpoint of the opposite side.__Angle Bisectors__:- Lines drawn from each vertex bisecting the opposite angle.

** 7. Area Formulas:- **

** (i) Using base and height:-**

** Area = 1/2 × base × height**

** (ii) Using Heron's formula for the area of a triangle with sides a, b, and c:-**

** Area = √s(s−a) (s−b) (s−c)**

** where s is the semiperimeter of the triangle defined as s = (a+b+c)/2.**

** 8. Similarity and Congruence:- Triangles can be similar (same shape, different size) or congruent (same shape and size).**

**Understanding these properties helps in solving geometric problems involving triangles and applying triangle properties in various fields of science, engineering, and mathematics.**