Triangle definition | Equilateral Isosceles Scalene and Acute angled Right angle Obtuse angled Triangle
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
In the given figure, ABC is a triangle in which AB = AC.
∴ △ABC is
an isosceles 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
(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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