NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Class 8: NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

The document NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 is a part of the Class 8 Course Additional Documents & Tests for Class 8.
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Understanding Quadrilaterals

Exercise 3.3

Question 1:
 Given a parallelogram ABCD. Complete each statement along with the definition or property used.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

(i) AD = ____________________
 (ii) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 DCB = ____________________
 (iii) OC = ____________________
 (iv) mNCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8DAB + mNCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8CDA = ____________________

Answer 1:
(i) AD = BC   [Since opposite sides of a parallelogram are equal]
(ii) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 DCB = NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 DAB  [Since opposite angles of a parallelogram are equal]
(iii) OC = OA    [Since diagonals of a parallelogram bisect each other]
(iv) mNCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8DAB + mNCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8CDA = 180o   [Adjacent angles in a parallelogram are supplementary]

Question 2:
 Consider the following parallelograms. Find the values of the unknowns x, y, ∠.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Note: For getting correct answer, read 3o= 30o in figure (iii)
(i) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 B + NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 C = 180o [Adjacent angles in a parallelogram are supplementary]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 100o+ x =180o
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x =180o-100o = 80o

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

and ∠= x = 80o    [Since opposite angles of a parallelogram are equal]
also y =100o     [Since opposite angles of a parallelogram are equal]
(ii) x +50o =180o    [Adjacent angles in a ||gm are supplementary]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x =180o- 50o =130o
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 ∠= x =130o [Corresponding angles]

(iii) x = 90o    [Vertically opposite angles]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 y + x +30o =180o  [Angle sum property of a triangle]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8
 [Alternate angles]

(iv) ∠= 80o   Corresponding angles]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x +80o = 180o  [Adjacent angles in a ||gm are supplementary]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x =180o- 80o = 100o             

and y = 80o    [Opposite angles are equal in a ||gm]

(v) y =112o [Opposite angles are equal in a ||gm]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 40o + y + x =180o [Angle sum property of a triangle]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 40o+112o+ x =180o
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 152o+ x =180o

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x =180o- 152o = 28o
and ∠= x = 28o [Alternate angles]

Question 3:
 Can a quadrilateral ABCD be a parallelogram, if:
 (i) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 D + NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 B = 180o
 (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
 (iii) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 A = 70o and NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 C = 65o

Answer 3:
(i) NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 D + NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 B = 180o
It can be, but here, it needs not to be.

  NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

(ii) No, in this case because one pair of opposite sides are equal and another pair of opposite sides are unequal. So, it is not a parallelogram.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

(iii) No. NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 A NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 C.
Since opposite angles are equal in parallelogram and here opposite angles are not equal in quadrilateral ABCD. Therefore it is not a parallelogram.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Question 4:
 Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

Answer 4:

ABCD is a quadrilateral in which angles NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 A = NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 C = 110o.

Therefore, it could be a kite.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

 

Question 5:
 The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.
 Answer 5
:
Let two adjacent angles be 3x and 2 . x
Since the adjacent angles in a parallelogram are supplementary.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 One angle = 3x = 3x36o =108o
and another angle = 2x = 2x36o = 72o

Question 6:
 Two adjacent angles of a parallelogram have equal measure. Find the measure of the angles of the parallelogram.

Answer 6:
Let each adjacent angle be x.
Since the adjacent angles in a parallelogram are supplementary.
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x + x =180o
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 2x =180o

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Question 7:
 The adjacent figure HOPW is a parallelogram. Find the angle measures x, y and ∠. State the properties you use to find them.

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Answer 7:

Here NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 HOP + 70o =180o[Angles of linear pair]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 HOP = 180o- 70o = 110o
and NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 E = NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 HOP [Opposite angles of a ||gm are equal]
NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 x =110o

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

∠ PHE = ∠HPO [Alternate angles]

∴ y = 400

Now ∠ EHO = ∠O = 70° [Corresponding angles]

=> 40° ∠ = 70°

=> ∠ = 70°- 40° = 30°

Hence,

x = 110° , y = 40° and ∠ =30°

Question 8: 

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

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

 

Answer 8:

(i) In parallelogram GUNS

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 
[ Opposite sides of parallelogram are equal]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

[ Opposite sides of parallelogram are equal]

Hence, x = 6cm, and y = 9 cm

(ii)  In parallelogram RUNS

y + 7 = 20 [ Diagonals of ||gm bisects each other]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Question 9: 

In the figure, both RISK and CLUE are parallelograms. Find the value of x. 

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Answer 9:

In Parallelogram RISK,

∠RIS = ∠K = 1200

[Opposite angles of A ||gm bisects each other]

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

∠m +120° = 180° [Linear pair]

=> ∠m = 180°-120° = 60°

and

=> ∠ ECI = ∠ L = 70° [Corresponding angles]

=> m + n + ∠ECl = 180° [Angle sum property of a triangle]

60°+n+ 70° = 180°

=> 130°+n = 180°

=> n= 180°-130° = 50°

also x = n = 50° [Vertically opposite angles]

Question 10: 

Explain how this figure is a trape∠ium. Which is its two sides are parallel? 

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Answer 10: 

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Here, M + L = 100° + 80 ° = 180° [Sum of interior opposite angles is 180°]

 NM and KL are parallel.

Hence, KLMN is a trapezium

Question 11: 

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Answer 11: 

Here, ∠B + ∠C = 1800 

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Question 12: 

Find the measure of ∠P and ∠S if SP || RQ in given figure.

(If you find mR is there more than one method to find m∠P)

NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8

Answer 12:

Here, ∠P + ∠Q = 180° [Sum of co-interior angles is 180° ]

=> ∠P + 130° = 180°

∠P = 180°-130°

=> ∠P = 50°

∴∠R = 900

∠S + 90° = 180° [Given]

∠S = 180°-90°

=> ∠s = 90°

Yes, one more method is there to find ∠P.

∠S+∠R+∠Q + ∠P = 360° [Angle sum property of quadrilateral]

90°+90° +130°+∠P = 360°

=> 310° + ∠P = 360°

=> ∠P = 360°-310°

=> ∠P = 50°

The document NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 Notes | Study Additional Documents & Tests for Class 8 - Class 8 is a part of the Class 8 Course Additional Documents & Tests for Class 8.
All you need of Class 8 at this link: Class 8

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