### 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]

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.

(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.

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 +

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,

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,

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 =

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 =

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 =

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 =