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**NCERT solutions for Class 8 Maths Understanding Quadrilaterals Download as PDF**

## NCERT Solutions for Class 8 Maths Understanding Quadrilaterals

**Class –VIII Mathematics (Ex. 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

(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]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 =

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]**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.

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.

**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 =

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

**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 =

And E = HOP

[Opposite angles of a gm are equal]PHE = HPO

[Alternate angles]Now EHO = O =

[Corresponding angles]Hence, and

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.

**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]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 =

NM and KL are parallel.

Hence, KLMN is a trapezium.

**11. Find ****C in figure , if **

**Ans. **Here, B + C =

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 =

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 =

## NCERT Solutions for Class 8 Maths Exercise 3.3

NCERT Solutions Class 8 Mathematics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 8 Mathematics includes text book solutions from Class 8 Maths Book . NCERT Solutions for CBSE Class 8 Maths have total 16 chapters. 8 Maths NCERT Solutions in PDF for free Download on our website. Ncert class 8 solutions PDF and Maths ncert class 8 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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