NCERT Solutions for Class 8 Chapter 3 Understanding Quadrilaterals -Free PDF Download

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Maths Revision Notes for Class 8

Chapter Name	Understanding Quadrilaterals
Chapter	Chapter 3
Exercise	Exercise 3.3
Class	Class 8
Subject	Maths NCERT Solutions
Board	CBSE
TEXTBOOK	CBSE NCERT
Category	NCERT Solutions

NCERT SOLVED

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

(i) AD = _______________

(ii) DCB = ______________

(iii) OC = _____________

(iv) DAB + CDA = ________

Ans. (i) AD = BC

$S i n c e o p p o s i t e s i d e s o f a p a r a l l e l o g r a m a r e e q u a l$

(ii) DCB = DAB

$S i n c e o p p o s i t e a n g l e s o f a p a r a l l e l o g r a m a r e e q u a l$

(iii) OC = OA

$S i n c e d i a g o n a l s o f a p a r a l l e l o g r a m b i s e c t e a c h o t h e r$

(iv) DAB + CDA =

$A d j a c e n t a n g l e s i n a p a r a l l e l o g r a m a r e s u p p l e m e n t a r y$

2. Consider the following parallelograms. Find the values of the unknowns

Note: For getting correct answer, read in figure (iii)

Ans. (i) B + C =

$A d j a c e n t a n g l e s i n a p a r a l l e l o g r a m a r e s u p p l e m e n t a r y$

And

$S i n c e o p p o s i t e a n g l e s o f a p a r a l l e l o g r a m a r e e q u a l$

Also

$S i n c e o p p o s i t e a n g l e s o f a p a r a l l e l o g r a m a r e e q u a l$

(ii)

[Adjacent angles in a gm are supplementary]

$C o r r e s p o n d i n g a n g l e s$

y = x = 130 degrees

$S i n c e o p p o s i t e a n g l e s o f a p a r a l l e l o g r a m a r e e q u a l$

(iii)

$V e r t i c a l l y o p p o s i t e a n g l e s$

$A n g l e s u m p r o p e r t y o f a t r i a n g l e$

$A l t e r n a t e a n g l e s$

(iv)

$C o r r e s p o n d i n g a n g l e s$

[Adjacent angles in a gm are supplementary]

And

[Opposite angles are equal in a gm]

(v)

[Opposite angles are equal in a gm]

$A n g l e s u m p r o p e r t y o f a t r i a n g l e$

And

$A l t e r n a t e a n g l e s$

3. Can a quadrilateral ABCD be a parallelogram, if:

(i) D + B =

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

(iii) A = and C =

Ans. (i) D + B =

It can be, but here, it needs to be a square or a rectangle.

(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.

(iii) No.A C.

Since opposite angles are equal in parallelogram and here opposite angles are not equal in quadrilateral ABCD. Therefore it is not a parallelogram.

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

Ans. ABCD is a quadrilateral in which angles A = C =

Therefore, it could be a kite.

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.

Ans. Let two adjacent angles be and

Since the adjacent angles in a parallelogram are supplementary.

One angle =

And Another angle =

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

Ans. Let each adjacent angle be

Since the adjacent angles in a parallelogram are supplementary.

Hence, each adjacent angle is

7. The adjacent figure HOPW is a parallelogram. Find the angle measures and State the properties you use to find them.

HOP +

Ans. Here HOP =

$A n g l e s o f l i n e a r p a i r$

And E = HOP

[Opposite angles of a gm are equal]

PHE = HPO

$A l t e r n a t e a n g l e s$

Now EHO = O =

$C o r r e s p o n d i n g a n g l e s$

Hence, and

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

Ans. (i) In parallelogram GUNS,

GS = UN

$O p p o s i t e s i d e s o f p a r a l l e l o g r a m a r e e q u a l$

Also GU = SN

$O p p o s i t e s i d e s o f p a r a l l e l o g r a m a r e e q u a l$

Hence, = 6 cm and = 9 cm.

(ii) In parallelogram RUNS,

[Diagonals of gm bisects each other]

And

Hence, cm and cm.

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

Ans. In parallelogram RISK,

RIS = K =

[Opposite angles of a gm are equal]

$L i n e a r p a i r$

And ECI = L =

$C o r r e s p o n d i n g a n g l e s$

$A n g l e s u m p r o p e r t y o f a t r i a n g l e$

Also

$V e r t i c a l l y o p p o s i t e a n g l e s$

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

Ans. Here, M + L =

[Sum of interior opposite angles is ]

NM and KL are parallel.

Hence, KLMN is a trapezium.

11. Find C in figure , if

Ans. Here, B + C =

[]

12. Find the measure of P and S if in given figure.

(If you find R is there more than one method to find P)

Ans. Here, P + Q =

[Sum of co-interior angles is ]

P +

P =

R = $G i v e n$

S +

S =

Yes, one more method is there to find P.

S + R + Q + P =

$A n g l e s u m p r o p e r t y o f q u a d r i l a t e r a l$

P =

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

NCERT Solutions for Class 8 Chapter 3 Understanding Quadrilaterals -Free PDF Download

NCERT SOLVED