NCERT Solutions for Class 8 Maths Exercise 3.1

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NCERT Solutions for Class 8 Maths Exercise 3.1 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 8 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Class 8 Maths Understanding Quadrilaterals Download as PDF

NCERT Solutions for Class 8 Maths Exercise 3.1

NCERT Solutions for Class 8 Maths Understanding Quadrilaterals

Class –VIII Mathematics (Ex. 3.1)
NCERT SOLUTION
1. Given here are some figures:

Classify each of them on the basis of the following:

(a) Simple curve   

(b) Simple closed curve

(c) Polygon    

(d) Convex polygon

(e) Concave polygon

Ans. (a) Simple curve

(b) Simple closed curve

(c) Polygons

(d) Convex polygons

(e) Concave polygon


2. How many diagonals does each of the following have?

(a) A convex quadrilateral  

(b) A regular hexagon

(c) A triangle

Ans. (a) A convex quadrilateral has two diagonals.

Here, AC and BD are two diagonals.

(b) A regular hexagon has 9 diagonals.

Here, diagonals are AD, AE, BD, BE, FC, FB, AC, EC and FD.

(c) A triangle has no diagonal.


NCERT Solutions for Class 8 Maths Exercise 3.1

3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try)

Ans. Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral in two triangles.

A + B + C + D

= 1 + 6 + 5 + 4 + 3 + 2

= (1 + 2 + 3) + (4 + 5 + 6)

=

[By Angle sum property of triangle]

=

Hence, the sum of measures of the triangles of a convex quadrilateral is

Yes, if quadrilateral is not convex then, this property will also be applied.

Let ABCD is a non-convex quadrilateral and join BD, which also divides the quadrilateral in two triangles.

Using angle sum property of triangle,

In ABD, 1 + 2 + 3 =  ……….(i)

In BDC, 4 + 5 + 6 =  ……….(i)

Adding eq. (i) and (ii),

1 + 2 + 3 + 4 + 5 + 6 =

 1 + 2 + (3 + 4) + 5 + 6

=

 A + B + C + D =

Hence proved.


NCERT Solutions for Class 8 Maths Exercise 3.1

4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
Figure
Side3456
Angle sum
What can you say about the angle sum of a convex polygon with number of sides?

Ans. (a) When  = 7, then

Angle sum of a polygon =

(b) When  = 8, then

Angle sum of a polygon =

(c) When  = 10, then

Angle sum of a polygon =

(d) When  =   then

Angle sum of a polygon =


NCERT Solutions for Class 8 Maths Exercise 3.1

5. What is a regular polygon? State the name of a regular polygon of:

(a) 3 sides 

(b) 4 sides  

(c) 6 sides

Ans. A regular polygon: A polygon having all sides of equal length and the interior angles of equal size is known as regular polygon.

(i)  3 sides

Polygon having three sides is called a triangle.

(ii)  4 sides

Polygon having four sides is called a quadrilateral.

(iii)  6 sides

Polygon having six sides is called a hexagon.


NCERT Solutions for Class 8 Maths Exercise 3.1

6. Find the angle measures  in the following figures:

Ans. (a) Using angle sum property of a quadrilateral,

 

 

 

(b) Using angle sum property of a quadrilateral,

 

 

 

(a) First base interior angle

=

Second base interior angle

=

There are 5 sides,  = 5

 Angle sum of a polygon =

=  =

 

 

 

 

 

(b) Angle sum of a polygon =

=  =

 

 

 

Hence each interior angle is


NCERT Solutions for Class 8 Maths Exercise 3.1

7. (a) Find     

(b) Find

Ans. (a) Since sum of linear pair angles is

 

 

And

 

Also

[Exterior angle property]

 

(b) Using angle sum property of a quadrilateral,

 

 

 

Since sum of linear pair angles is

   ……….(i)

  ……….(ii)

  ……….(iii)

  ……….(iv)

Adding eq. (i), (ii), (iii) and (iv),

 

 

 

 


NCERT Solutions for Class 8 Maths Exercise 3.1

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