Triangle
Category : 4th Class
The geometrical shapes having three sides are called triangles.
Properties of a Triangle
Types of Triangle
Triangles are classified:
Side Based Classification
On the basis of sides, triangles have been classified into three groups
Equilateral Triangle
A triangle whose all sides are of equal length is called equilateral triangle.
Note: All the angles of an equilateral triangle are of \[\text{6}0{}^\circ \].
\[\Delta \text{ABC}\] is an equilateral triangle as AB = BC = AC = 4 cm In triangle ABC,\[\angle \text{ABC}=\angle \text{BCA}=\angle \text{CAB}=\text{6}0{}^\circ \].
Isosceles Triangle
A triangle whose any two sides are of equal length are called isosceles triangle. Note: Opposite angles of equal sides of a isosceles triangle are equal.
\[\Delta \text{ABC}\] is a isosceles triangle as AB = AC= 4 cm. In \[\Delta \text{ABC}\],\[\angle \text{ABC}=\angle \text{BCA}=\text{7}0{}^\circ \]
Scalene Triangle
A triangle whose all sides are of different length is called scalene triangle.
Note: No angles are equal in a scalene triangle.
\[\Delta \text{PQR}\] is a scalene triangle as\[PQ\ne QR\ne PR\] In\[\Delta \text{PQR}\], \[\angle PQR\ne \angle QRP\ne \angle RPQ\]
Angle Based Classification
On the basis of angles, triangles are of three types:
Acute - Angled Triangle
The triangles having all angles between \[\text{9}0{}^\circ \]and\[0{}^\circ \] are called acute-angled triangle.
ABC is an acute - angled triangles as its every angles\[(\angle A,\angle B,\angle C)\]measures between\[0{}^\circ \] and\[\text{9}0{}^\circ \].
Right-Angled Triangle
The triangles having an angle of 90° are called a right-angled triangle.
\[\Delta ABC\] is a right - angled triangle as it contains a right angle \[(\angle ABC)\].
Obtuse Angled Triangle
The triangles having one obtuse angle are called obtuse - angled triangles.
\[\Delta MNP\] is an obtuse - angled triangle as it contains an obtuse angle \[(\angle MNP)\].
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