4th Class Mathematics Geometrical Figures Triangle

  Triangle

The geometrical shapes having three sides are called triangles.

Properties of a Triangle

• A triangle has three sides.
• A triangle has three angles.
• A triangle has three vertexes.
• Sum of all the three angles of a triangle is\[\text{18}0{}^\circ \].

• Three sides of the triangle ABC are AB, BC, and CA
• Three angles of the triangle are\[\angle \text{ABC}\], \[\angle \text{BCA}\], and \[\angle \text{CAB}\]
• Three vertexes of the triangle are point A, point B, and point C
• Sum of the all three angles of the triangle ABC, \[\angle \text{ABC}+\angle \text{BCA}+\angle \text{CAB}\] \[=\text{6}0{}^\circ +\text{4}0{}^\circ +\text{8}0{}^\circ =\text{18}0{}^\circ \]

Types of Triangle

Triangles are classified:

• On the basis of sides.
• On the basis of angles.

Side Based Classification

On the basis of sides, triangles have been classified into three groups

• Equilateral triangle
• Isosceles triangle
• Scalene triangle

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
• Right - angled triangle
• Obtuse - angled triangle

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 \[(\angle MNP)\].