4th Class Mathematics Geometrical Figures Triangle

Triangle

Category : 4th Class

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 $(\angle MNP)$.

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