Understanding Quadrilaterals - Solutions 3
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 3
Understanding Quadrilaterals (Ex. 3.3)
NCERT Solutions
CHAPTER - 3
Understanding Quadrilaterals (Ex. 3.3)
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
[Since opposite sides of a parallelogram are equal]
(ii)
DCB =
DAB


[Since opposite angles of a parallelogram are equal]
(iii) OC = OA
[Since diagonals of a parallelogram bisect each other]
(iv)
DAB +
CDA = 



[Adjacent angles in a parallelogram are supplementary]
2. Consider the following parallelograms. Find the values of the unknowns 











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

Ans. (i)
B +
C = 



[Adjacent angles in a parallelogram are supplementary]








And 

[Since opposite angles of a parallelogram are equal]
Also 

[Since opposite angles of a parallelogram are equal]
(ii) 

[Adjacent angles in a
gm are supplementary]









[Corresponding angles]

[Since opposite angles of a parallelogram are equal]
(iii) 

[Vertically opposite angles]






[Angle sum property of a triangle]








[Alternate angles]
(iv) 

[Corresponding angles]


[Adjacent angles in a
gm are supplementary]







And 

[Opposite angles are equal in a
gm]

(v) 

[Opposite angles are equal in a
gm]







[Angle sum property of a triangle]






And 

[Alternate angles]
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.

(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.



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.



Since the adjacent angles in a parallelogram are supplementary.








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 = 


[Angles of linear pair]
And
E =
HOP


[Opposite angles of a
gm are equal]





[Alternate angles]


Now
EHO =
O = 



[Corresponding angles]




Hence,
and 


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


Ans. (i) In parallelogram GUNS,




Ans. (i) In parallelogram GUNS,
GS = UN
[Opposite sides of parallelogram are equal]




Also GU = SN
[Opposite sides of parallelogram are equal]








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,


Ans. In parallelogram RISK,



[Opposite angles of a
gm are equal]




And
ECI =
L = 



[Corresponding angles]


[Angle sum property of a triangle]







Also 

[Vertically opposite angles]
10. Explain how this figure is a trapezium. Which of its two sides are parallel?

Ans. Here,
M +
L = 

Ans. Here,



[Sum of interior opposite angles is
]


Hence, KLMN is a trapezium.
11. Find
C in figure , if 

Ans. Here,
B +
C = 



Ans. Here,



[
]






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 = 



Ans. Here,



[Sum of co-interior angles is
]






















Yes, one more method is there to find
P.






[Angle sum property of quadrilateral]








