Triangle definition | Equilateral Isosceles Scalene and Acute angled Right angle Obtuse angled Triangle

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Triangle

A plane figure bounded by three line segments is called triangle. 
We denote a triangle by the symbol△  .

A △ABC has:
(i)         Three vertices, namely A, B and C.
(ii)        Three sides, namely AB, BC and CA.
(iii)       Three angles, namely ∠A, ∠B and ∠C. 
A triangle has six parts— three sides and three angles

Type of Triangles:

    1.       On the basis of sides:

(i). Equilateral Triangle: A triangle having all sides equal is called an equilateral triangle.

In the given figure, ABC is a triangle in which AB = BC = CA.
∴     △ABC is an equilateral triangle.
(ii). Isosceles Triangle: A triangle having two sides equal is called an isosceles triangle.

In the given figure, ABC is a triangle in which AB = AC.
∴     △ABC is an isosceles triangle.
(iii). Scalene Triangle: A triangle in which all the sides are of different length is called a scalene triangle.
In the given figure, PQR is a triangle. In which PQ ≠ QR ≠ PR.
∴     △PQR is a scalene triangle.

    2.       On the basis of angles:

(i). Acute-angled Triangle: A triangle in which every angle measures more than 00 but less than 900 is called an acute angled triangle.

In the given figure, ABC is a triangle in which every angle is an acute angle.
∴     △ABC is an acute-angled triangle.
(ii). Right-angled triangle: A triangle in which one of the angles measures 900 is called a right-angled triangle or simply a right triangle.
In a right-angled triangle, the side opposite to the right angle is called its hypotenuse and the remaining two sides are called its legs.

In the given figure,  △ABC is a right triangle in which , AC is the hypotenuse, and AB, BC are its legs.
(iii). Obtuse-angled triangle: A triangle in which one of the angles measures more than 900 but less than 1800 is called an obtuse-angled triangle.

In the given figure, PQR is a triangle in which ∠PQR is an obtuse angle.
∴     △PQR is an obtuse-angled triangle.

Perimeter of a triangle: The sum of the lengths of three sides of a triangle is called its perimeter.

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