Understanding Quadrilaterals - Solutions 3

CBSE Class –VIII Mathematics
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]
y = x = 130 degrees
[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.
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 = 
[Angles of linear pair]
And E = HOP
[Opposite angles of a gm are equal]
PHE = HPO
[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,
GS = UN
[Opposite sides of parallelogram are equal]
cm
Also GU = SN
[Opposite sides of parallelogram are equal]
cm
Hence, = 6 cm and = 9 cm.
(ii) In parallelogram RUNS,
[Diagonals of gm bisects each other]
cm
And 
cm
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]
[Linear pair]
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 = 
[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 = 
P = 
R = [Given]
S + 
S = 
S = 
Yes, one more method is there to find P.
S + R + Q + P = 
[Angle sum property of quadrilateral]
P = 
P =