5th Class Mathematics Geometrical Figures Angle

     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 (\[\angle MNP\])