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

Free PDF download of NCERT Solutions Maths Class 8 Solutions Chapter 3 – Understanding Quadrilaterals solved by Expert Maths Teachers on CoolGyan.Org. All Chapter 3 – Understanding Quadrilaterals Questions with Solutions for NCERT to help you to revise complete Syllabus and Score More marks.

Maths Revision Notes for Class 8

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

[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 =