Understanding Quadrilaterals| NCERT Solutions| Class 8

NCERT Solutions of  Chapter: Understanding Quadrilaterals|. NCERT Solutions along with worksheets and notes for Class 8.

Exercise 3.1

 (1) Given here are some figures.

 

Diagram of Question 1 of Exercise 3.1 of NCERT Chapter Understanding Quadrilaterals                                      

1                                         2                                          3

                                           

4                                        5                                             6

                          

7                                      8

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-

SN Basis of classification Number of figure
(a) Simple curve 1, 2, 5, 6, 7
(b) Simple closed curve 1,2, 5, 6, 7
(c) Polygon 1, 2
(d) Convex polygon 2
(e) Concave polygon 1

 

(2) How many diagonals does each of the following have?

(a) A convex quadrilateral  (b) A regular hexagon (c) A triangle

Ans-

(a)

 

Diagram of Question 2(a) of Exercise 3.1 of NCERT Chapter Understanding Quadrilaterals

ABCD is a convex quadrilateral.

AC and BD are two diagonals.

(b) A regular hexagon

 

Diagram of Question 2(b) of NCERT Chapter Understanding Quadrilaterals

ABCDEF is a regular hexagon.

AC, AE, AD, BD, BF, BE, CE, CF and DE are diagonals.

(c) A triangle

Diagram of Question 2(c) of Exercise 3.1 of NCERT Chapter Understanding Quadrilaterals

ABC is a triangle.

Triangle does not have any diagonals because there are no two non – consecutive vertices. All vertices of triangle are consecutive. So, any two vertices cannot be connected to draw diagonal.

AB, AC and BC are sides of triangle. A, B and C are consecutive vertices of triangle.

 

(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-

(i)

 

Diagram of Question 3 of Exercise 3.1 of NCERT Chapter Understanding Quadrilaterals

Ans

(5) What is a regular polygon?

State the regular polygon?

State the name of a regular polygon of

(i) 3 sides (ii) 4 sides   (iii) 6 sides

Ans-

The polygons that have equal lengths and equal angles are called regular polygons.

Eg:- An equilateral triangle[It has equal sides and equal angles]

Name of the regular polygon according to their sides

S.N. Sides of regular polygon Name of the regular polygon
(i) 3 Triangle
(ii) 4 sides Quadrilateral
(iii) 6 sides Hexagon

 

(6) Find the angle measure x in the following figures:

 

Diagram of Question 6(a) of Exercise 3.1 of Chapter NCERT Understanding Quadrilaterals          Diagram of Question 6(b) of Exercise 3.1 of Chapter NCERT Understanding Quadrilaterals

a                                                                    b

Diagram of Question 6(c) of Exercise 3.1 of Chapter NCERT Understanding Quadrilaterals                             Diagram of Question 6(d) of Exercise 3.1 of Chapter NCERT Understanding Quadrilaterals

c                                                                                            d

Ans-

(a)

 

 

(b)

 

(c)

 

(d)

 

(7)

(a)Find x + y + z

 

Diagram of Question 7(a) of NCERT Chapter Understanding Quadrilaterals

(b)Find x + y + z + w

 

Diagram of Question 7(b) of NCERT Chapter Understanding Quadrilaterals

Ans-

(a)

 

 

(b)

 

Exercise 3.2

(1) Find x in the following figures.

 

Diagram of Question 1(a) of Exercise 3.2 of NCERT Chapter Understanding Quadrilaterals                         Diagram of Question 1(b) of Exercise 3.2 of NCERT Chapter Understanding Quadrilaterals

a                                                                                         b

Ans-

(a)

 

 

(b)

 

ii

(5) (a) Is it possible to have a regular polygon with measure of each exterior angle as 220?

(b) Can it be an interior angle of a regular polygon? Why?

Ans-

(a)

Understanding quadrilaterals,A 5(a),Ex 3.2,NCERT,class 8

(b)

 

Diagram of Question 1(i) of Exercise of 3.3 of NCERT Chapter Understanding Quadrilaterals                   Diagram of Question 1(ii) of Exercise of 3.3 of NCERT Chapter Understanding Quadrilaterals

i                                                                          ii

Diagram of Question 1(iii) of Exercise of 3.3 of NCERT Chapter Understanding Quadrilaterals

iii

Diagram of Question 1(iv) of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

iv

Diagram of Question 1(v) of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

v

Ans-

(i)

(ii)

 

(iii)

 

(iv)

 

(v)

 

(i)

 

(a) It has four sides.

Satisfied.

(b)Its opposite sides are parallel and equal in length.

Donot know

(c)The opposite angles of a parallelogram are of equal measure.

Donot know

(d) The adjacent angles in a parallelogram are supplementary.

Satisfied. A + C and D + B are adjacent and supplementary.

(e) The diagonals of a parallelogram bisect each other at the point of intersection.

Satisfied.

But all conditions for a parallelogram are not satisfied. Hence, it need not be a parallelogram, but it can be.

(ii) AB = DC = 8cm, AD = 4 cm, and BC = 4.4 cm?

In a quadrilateral ABCD
AB = DC = 8cm

AD = 4 cm

BC = 4.4 cm

In a parallelogram opposite sides are equal in length.

But,

AD and BC are opposite and not equal sides.

Hence, it can not be a parallelogram.

(iii) ∠A = 700 and ∠C = 650

In a quadrilateral ABCD

Opposite angles ∠A = 700 and ∠C = 650 are not equal.

Hence, it can not be a parallelogram.

 

(4) Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

Ans-

A quadrilateral that is not parallelogram but has exactly two opposite angles of equal measure is kite.

In figure below ABCD is a kite.

schoolhelpbygunjan.wordpress.com | Understanding quadrilaterals | Diagram | Kite | NCERT | Class 8

(6) Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Ans-

 

Diagram of Question 6 Of Exercise 3.3 of NCERT Understanding Quadrilaterals

(7) The adjacent figure HOPE is a parallelogram. Find the angle measure x, y and z. State the properties you to find them.

Ans-

 

Diagram of Question 7 Of Exercise 3.3 of NCERT Understanding QuadrilateralsAns

(8) The following figures GUNS and RUNS are parallelograms. Find x and y.(Lengths are in cm)

Ans-

 

Diagram of Question 8(i) Of Exercise 3.3 of NCERT Understanding QuadrilateralsDiagram of Question 8(ii) Of Exercise 3.3 of NCERT Understanding Quadrilaterals

i                                                                                   ii

Ans-

(i)

 

(ii)

 

y = 20 -7

y = 13

RO = ON

16 = x + y

Or

x + y = 16

Putting value of y

x + 13 = 16

Transposing 13 to RHS

x = 1 6– 13

x = 3

Hence, x = 3 and y = 13.

 

(9) In the given figure both RISK and CLUE are parallelograms. Find the value of x.

 

Diagram of Question 9 of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

Ans-

(10) Explain how this figure is a trapezium. Which of its two sides are parallel?

 

Diagram of Question 10 of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

Ans-

Diagram of Question 11 of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

Ans-

Diagram of Question 12 of Exercise 3.3 of NCERT Chapter Understanding Quadrilaterals

Ans-

Exercise 3.4

(1) State whether True and False.

(a) All rectangles are squares.

(b) All rhombuses are parallelograms.

(c) All squares are rhombuses and also rectangles.

(d) All squares are not parallelograms.

(e) All kites are rhombuses.     

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.   

Ans-

(a) All rectangles are squares.   False

(b) All rhombuses are parallelograms.    True

(c) All squares are rhombuses and also rectangles.   True

(d) All squares are not parallelograms.    False

(e) All kites are rhombuses.     False

(f) All rhombuses are kites.   True

(g) All parallelograms are trapeziums.   True

(h) All squares are trapeziums.   True

 

(2) Identify all the quadrilaterals that have.

(a) four sides of equal length

(b) four right angles

Ans-

(a) four sides of equal length

(i) Square

(ii) Rhombus

(b) four right angles

(i) Square

(ii)Rectangle

 

(3) Explain how a square is.

(i) a quadrilateral  (ii) a parallelogram   (iii) a rhombus    (iv) a rectangle

Ans-

 

Diagram of Question 3 of Exorcise 3.4 of NCERT chapter Understanding Quadrilaterals

(i)

(ii)

 

(iii)

 

(iv)

 

(4) Name the quadrilaterals whose diagonals.

(i) bisect each other   (ii) are perpendicular bisectors of each other   (iii) are equal

Ans-

(i) The quadrilaterals whose diagonals bisect each other

(a) Parallelogram

(b) Rhombus

(c) Square

(d)Rectangle

(ii) The quadrilaterals whose diagonals are perpendicular bisectors of each

(a) Rhombus

(b) Square

(iii) The quadrilaterals whose diagonals are equal

(a)Rectangle

(b) Square

 

(5) Explain why a rectangle is a convex quadrilateral.

Ans-

 

Understanding quadrilaterals,diagram ,A 5,Ex 3.4,NCERT,class 8

Let ABCD is a rectangle.

AB, BC, CD and DA are sides of it.

AC and BD are diagonals of it.

Both diagonal lies inside the rectangle.

Hence, a rectangle is a convex quadrilateral.

 

(6) ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

 

Diagram of Question 6 of Exercise 3.4 of NCERT Chapter Understanding Quadrilaterals

Ans

Helping Topics

Understanding Quadrilaterals

Worksheet Class 8

 

 

 

 

 

 

 

 

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