Class 8 Maths Chapter 3 Introduction Understanding Quadrilaterals NCERT

 

 CHAPTER 3

Understanding Quadrilaterals

Class 8 Maths Chapter 3 Understanding Quadrilaterals NCERT

 Download PDF

Class 8 Maths Chapter 3 Understanding Quadrilaterals NCERT

Video and Solutions

ONLINE CLASS 

Exercise 3.1

Given here are some figures : 

Q1. Given are some figures. Classify each of them on the basis of the following:

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

Answer : 

Figure No. Description / Type Classification

(1) Closed figure made of straight lines, with one interior angle greater than 180° Concave polygon

(2) Closed figure made of straight lines, all angles less than 180° Convex polygon

(3) Closed curved figure (two ovals) Simple closed curve

(4) Star shape (crossing lines) Polygon (not simple)

(5) Two circles joined, boundary crosses itself Not a simple curve

(6) Closed curved figure (like capsule shape) Simple closed curve

(7) Closed figure with straight and curved edges, one inward angle Concave polygon

(8) Line with two ovals (open shape) Simple curve (open)

Q2. What is a regular polygon?

Answer:

A regular polygon is a polygon that has all sides equal in length and all angles equal in measure.

Q3. State the name of a regular polygon of:

(i) 3 sides  (ii) 4 sides  (iii) 6 sides  

Answer : 

(i) 3 sides - Equilateral triangle

(ii) 4 sides - Square

(iii) 6 sides - Regular hexagon

Exercise 3.2

1. Find x in the following figures.

2. Find the measure of each exterior angle of a regular polygon of

(i) 9 sides (ii) 15 sides

3. How many sides does a regular polygon have if the measure of an exterior angle is 24°?

4. How many sides does a regular polygon have if each of its interior angles

is 165°?

5. (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

(b) Can it be an interior angle of a regular polygon? Why?

6. (a) What is the minimum interior angle possible for a regular polygon? Why?

(b) What is the maximum exterior angle possible for a regular polygon?

(ii) 4 sides -

EXERCISE 3.3

 1. Given a parallelogram ABCD. Complete each

statement along with the definition or property used.

(i) AD = ...... (ii) ∠ DCB = ......

(iii) OC = ...... (iv) m ∠DAB + m ∠CDA = ......

Solution :

(i) AD = BC

Opposite sides of a parallelogram are equal.

(ii) ∠ DCB = ∠ DAB

Opposite sides of a parallelogram are equal.

(iii) OC = OA 

Diagonals of a parallelogram bisect each other.

(iv) m ∠DAB + m ∠CDA = 180°

Adjacent angles of a parallelogram are supplementary.

2. Consider the following parallelograms. Find the values of the unknowns x, y, z.

Solution :

(i) y = 100°

Opposite angles of a parallelogram are equal.

x + 100° = 180°

Adjacent angles in a parallelogram are supplementary.

=> x =  180° - 100°

=> x = 80°

=> z = x = 80°

Opposite angles of a parallelogram are equal.

3. Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180°? 

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) ∠A = 70° and ∠C = 65°?

Solutions : 

(i) Can be but not need be.

(ii) No, because in a parallelogram, opposite sides are equal but here  AD ⍯ BC

(iii) No, because in a parallelogram, opposite angles are of equal  measure but here  ∠A ⍯ ∠C

4. Draw a rough figure of a quadrilateral that is not a  parallelogram but has exactly two opposite angles of equal measure.

Solutions : 

5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

Solutions : 

6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Solutions : 

7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Solutions : 

8. The following figures GUNS and RUNS are parallelograms.

Find x and y. (Lengths are in cm)

Solutions : 

9. 

In the above figure both RISK and CLUE are parallelograms. Find the value of x.

Solutions : 

10. Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.26)

Solutions : 

11. Find m∠C in Fig 3.27 if AB DC

Solutions : 

    

12. Find the measure of ∠P and ∠S if SP RQ  in Fig 3.28.

(If you find m∠R, is there more than one method to find m∠P?)

Solutions : 

    

We hope the NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex. 3.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex. 3.3 drop a comment below and we will get back to you at the earliest.