Geometry of Class 5 to Class 8

     

Geometry of Class 5 to Class 8

What is Geometry?

• Answer:-Geometry is a branch of mathematics where  size, shape, perimeter,area, volume of matter is discussed or studied.

• Today in this article I will try to explain about triangles and quadrilaterals.This will be beneficial for on going school students of class 5 to class 8. 

       

   

   What is triangle? 

•  Answer:-A closed shape which is bounded by three sides, having three vertices, three angles in a plane is termed as triangle.

 

       In the figure ABC is a triangle

• What are the different types of triangles? Discuss elaborately.

   

  Answer:

         

•  Triangles are divided in 6 different types:-
   
   On the basis of sides triangles are divided in three different types and they are namely—- a) Equilateral triangle.b) Isosceles triangle c)Scalene triangle.

• Again on the basis of angles triangles are divided in three different types and they are namely—--1)Acute angled triangle 2) Obtuse angled triangle 3) Right angled triangle

• Equilateral triangle:-

• A triangle whose all sides also all angles are equal i.e equal in measure is called an Equilateral triangle.

• In the figure; ABC is anequilateral triangle whose AB=BC=AC also <A =<B=<C=60°

   

• Isosceles triangle:-

• A triangle whose any two sides are equal i.e; equal in measure is termed as isosceles triangle.

 

• In the figure, triangle PQR is an isosceles triangle whose PQ=QR=6 cm

•  Scalene triangle:- 

• A triangle whose all three sides are different i.e; measure different is known as scalene triangle. 

•  In the figure, XYZ is a scalene triangle,whoseXY=4cm,XZ=2cmYZ=3cm

Acute angled triangle:-

• A triangle whose all three angles are acute i e; measures less than 90 degree is called acute angled triangle. 
• 
  

  

• In the figure,PQR is an acute angled triangle whose <P=80 degree <Q=40 degree and<R=60 degree.

Obtuse angled triangle:- 

• A triangle whose any one angle measure more than 90 degree is called is termed as Obtuse angled triangle.
• 
  

• In the figure; LMN is an Obtuse angled triangle,whose<M=120degree

  •Right angled triangle:-- 

A triangle whose any one angle measure 90 degree is known as right angled triangle.

 

In the fig; PQR is a right angled triangle,whose<Q =90°

   What is a quadrilateral? 

•  Answer:-A geometrical shape which is bounded by four sides, having four angles,four vertices is known as quadrilateral.

 

•      In the figure PQRS is a quadrilateral.

• What are the different types of quadrilateral? Discuss elaborately. 

• Answer: Quadrilaterals are of 6 types and they are:-1) Parallelogram 2) Rectangle 3) Square 4) Rhombus 5) Trapezium 6)Kite. 

•  Parallelogram:-

• A quadrilateral whose opposite sides are equal and parallel,opposite angles are equal, diagonals bisect each other at their point of contact is called parallelogram.

     
 

•      In the figure ABCD is a parallelogram Whose AB=CD, AD=BC;<A=<C, <B=<D

      

        

• Rectangle:- 

• A quadrilateral whose opposite sides are equal and parallel, opposite angles are equal,both diagonals are equal and bisect each other, each angle measure 90 degree is called rectangle.

     

•      In the figure; MNOP is a rectangle whose MN=OP, MP=ON and <M=<N=<O=<P=90 degree

• Square:- 

• A quadrilateral whose all sides are equal in measure, all angles measure 90 degree, have two equal diagonals and they bisect each other perpendicularly is called square.

 

•     In the figure, ABCD is a square whose AB=BC=CD=AD ;and <A=<B=<C =<D=90degree

• Rhombus:- 

• A quadrilateral whose all sides are equal and diagonals bisect each other at right angles is termed as rhombus.

 

•    In the figure WXYZ is rhombus, whose XY=YZ=WZ=XW; also YW perpendicular XZ 
                   
•                                                                                                                                              

• Trapezium:- 

• A quadrilateral whose only one pair of side is parallel is called trapezium.

   

In the trapezium MNOP, OP|| MN

• Kite:- 

• A quadrilateral whose adjacent sides are equal is called a kite.

 

In the above kite ABCD, AB=AD; BC=CD
     

• Note:- Some measurements of sides and angles are approximate values have been used just for convenience purpose, students are advised to draw accurate measurements of angles and sides using protractor and scale.

FREQUENTLY ASKED QUESTIONS:-

What is the measure of each exterior angle of a polygon which has n number of sides?

Answer: The measure of each exterior angle of a polygon = 360°/n

What is the sum of all exterior angles of a polygon?

Answer:- The sum of all exterior angles of a polygon = 360°

What is the sum of all interior angles of a polygon which has 'n' number of sides?

Answer :- The sum of all interior angles = (2n - 4) × 90°

How many right angle can have a triangle?

Answer :- A triangle can have only one right angle.

What is the least measure of an exterior angle of a polygon.

Answer:- 120°

How many altitude can have a triangle?

Answer:- A triangle can have 3 altitude.

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