5th Class Mathematics Geometrical Figures Angle

Angle

Category : 5th Class

*     Angle

 

 

Inclination between two rays having common end point is called angle.

 

 

In the above given picture, OA and OB are two rays which have a common end point 0. Point 0 is called vertex and rays OA and OB are called arms. The inclination between the rays OA and OB is called angle AOB, and it is denoted as \[\angle \text{AOB}\text{.}\]

 

 

Angle is measured in degree. Symbol of the degree is \[~{{''}^{o}}''\] and written as \[{{a}^{o}}.\]  

 

 

*  Types of Angle     

There are different types of angles.

(a) Acute angle                   

(b) Right Angle

(c) Obtuse angle                  

(d) Straight angle

 

 

*Acute Angle

An angle which measures between 0° and 90° is called acute angle.

 

 

 

Measure the given below angle and find is it an acute angle.


               

 

Explanation                

Measure of the above given angle is \[{{40}^{o}}.\]

Therefore, the angle is an acute angle  

 

* Right Angle

An angle of \[{{90}^{o}}\] is called right angle.

 

 

 

*  Obtuse Angle

An angle which measures between \[{{90}^{o}}\] and \[{{180}^{o}}\] is called obtuse angle.

 

 

 

* Straight Angle                

An angle which measures \[{{180}^{o}}\] is called straight angle.  

 

 

 

*  Triangle

The geometrical shapes having three sides are called triangle.

 

 

 

 

* Properties of Triangle

Triangle has:

(i) Three sides,                                 

(ii) Three angles                                     

(iii) Three vertices

 

 

Three sides of the triangle \[\text{XYZ}\]are\[\text{ }\!\!~\!\!\text{ XY, YZ,}\] and \[\text{ZX}\]

Three angles of the triangle are \[\angle \text{X,}\angle \text{Y,}\]and \[\angle Z\]

Three vertices of the triangle are point \[\text{X,}\] point Y, and point Z.  

 

 

* Types of Triangle

Triangle has been classified:

(a) On the basis of sides

(b) On the basis of angles  

 

 

* Sides Based Classification

On the basis of sides, triangles are of three types

(i) Equilateral Triangle

(ii) Isosceles Triangle

(iii) Scalene Triangle  

 

 

* Equilateral Triangle

A triangle whose all sides are of equal length is called equilateral triangle.

 

\[\Delta \] ABC is an equilateral triangle as AB = BC = AC = 4 cm.

Note: All the angles of an equilateral triangles are of  \[{{60}^{o}}\]  

 

 

* Isosceles Triangle

A triangle whose any two sides are of equal length is called isosceles triangle.

 

 

\[\Delta \] ABC is an isosceles triangle as AB = AC 5 cm.

Note: In an isosceles triangle, opposite angles of equal sides are equal  

 

 

* Scalene Triangle    

A triangle whose all sides are of different length is called scalene triangle.

 

 

\[\Delta \] PQR is a scalene triangle as \[PQ\ne QR\ne PR.\]

Note: In a scalene triangle, no angles are equal  

 

 

* Angle Based Classification

On the basis of angles, triangle are of three types

(i) Acute-angled Triangle

(ii) Right-angled Triangle

(iii) Obtuse-angled Triangle  

 

 

*Acute-Angled Triangle

A triangle having all angles between 90° and 0° is called acute-angled triangle.

 

ABC is an acute-angled triangle as its each angle (\[\angle A,\angle B,\angle C\]) measures between \[{{0}^{o}}\] and \[{{90}^{o}}.\]  

 

 

* Right-Angled Triangle

A triangle having an angle of 90° is called a right-angled triangle.

 

 

\[\Delta \]ABC is a right-angled triangle as it contains a right angle(\[\Delta ABC\])  

 

 

* Obtuse-Angled Triangle

A triangle having one obtuse angle is called obtuse-angled triangle.

 

 

\[\Delta \]MNP is an obtuse-angled triangle as it contains an obtuse angle (\[\angle MNP\])  

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