Class 8 Exam  >  Class 8 Notes  >  NCERT Solution (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Understanding Quadrilaterals

Exercise 3.3

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

(i) AD = ____________________
 (ii) NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths DCB = ____________________
 (iii) OC = ____________________
 (iv) mNCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, MathsDAB + mNCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, MathsCDA = ____________________

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

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths x =180o- 50o =130o
NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths ∠= x =130o [Corresponding angles]

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths
 [Alternate angles]

(iv) ∠= 80o   Corresponding angles]

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 40o + y + x =180o [Angle sum property of a triangle]
NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 40o+112o+ x =180o
NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 152o+ x =180o

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths x =180o- 152o = 28o
and ∠= x = 28o [Alternate angles]

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

Answer 3:
(i) NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths D + NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths B = 180o
It can be, but here, it needs not to be.

  NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

(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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

(iii) No. NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths A NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, MathsNCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths A = NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths C = 110o.

Therefore, it could be a kite.

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

 

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths x + x =180o
NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 2x =180o

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Answer 7:

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

∠ 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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

 

Answer 8:

(i) In parallelogram GUNS

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths 
[ Opposite sides of parallelogram are equal]

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

[ 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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Question 9: 

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Answer 9:

In Parallelogram RISK,

∠RIS = ∠K = 1200

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

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

∠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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Answer 10: 

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

Answer 11: 

Here, ∠B + ∠C = 1800 

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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 Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

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°

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FAQs on NCERT Solutions for Class 8 Maths - (Ex- 3.3) - Chapter 3: Understanding Quadrilaterals, Maths

1. What are the different types of quadrilaterals?
Ans. There are different types of quadrilaterals, such as square, rectangle, parallelogram, rhombus, kite, and trapezium, that have different properties and characteristics.
2. How do we differentiate between a square and a rectangle?
Ans. A square is a special type of rectangle that has all sides equal. A rectangle has opposite sides equal and all angles equal to 90 degrees. Therefore, if all sides of a rectangle are the same, it becomes a square.
3. Can a quadrilateral have exactly one pair of parallel sides?
Ans. Yes, a trapezium is a quadrilateral that has only one pair of parallel sides. The other two sides are non-parallel and of different lengths.
4. How can we find the area of a parallelogram?
Ans. The area of a parallelogram can be found by multiplying the base and the height of the parallelogram. The height is the perpendicular distance between the two parallel sides.
5. What is the sum of the interior angles of a quadrilateral?
Ans. The sum of the interior angles of a quadrilateral is equal to 360 degrees.
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