Understanding Quadrilaterals Exercise 3.3

NCERT SOLUTION

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]

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NCERT Solutions for Class 8 Maths Exercise 3.3

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]

(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]

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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 not to be.

(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.

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NCERT Solutions for Class 8 Maths Exercise 3.3

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.

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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 =

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NCERT Solutions for Class 8 Maths Exercise 3.3

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

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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

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NCERT Solutions for Class 8 Maths Exercise 3.3

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.

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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]

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NCERT Solutions for Class 8 Maths Exercise 3.3

10. Explain how this figure is a trapezium. Which is 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.

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11. Find C in figure , if

Ans. Here, B + C =

[]

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NCERT Solutions for Class 8 Maths Exercise 3.3

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 =