Class 8 Understanding Quadrilaterals

Ex 3.1

1. Given here 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
2. What is a regular polygon?State the name of a regular polygon of(i) 3 sides (ii) 4 sides (iii) 6 sides

                                                                            Ex 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? 

Chapter 3: Ex 3.1 and Ex 3.2 Understanding Quadrilaterals Free PDF

                                                                         Ex 3.3

1. Given a parallelogram Abcd. Complete each statement along with the definition or property used.

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

(I)

(ii) 

(iii) 

(iv) 

(v)

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°? 

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

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. 

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

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

8. The following figures GUNS and RUNS are parallelograms.Find x and y. (Lengths are in cm)

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

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

11. Find m∠C in Fig 3.27 if AB|| DC
 

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?)

Chapter 3: Ex 3.3 Understanding Quadrilaterals Free PDF

Ex 3.4 1. State whether True or False. 

(a) All rectangles are squares 

(b) All rhombuses are parallelograms 

(c) All squares are rhombuses and also rectangles 

(d) All squares are not parallelograms. 

(e) All kites are rhombuses.

 (f) All rhombuses are kites. 

(g) All parallelograms are trapeziums. 

(h) All squares are trapeziums. 

2. Identify all the quadrilaterals that have. 

(a) four sides of equal length (b) four right angles 

3. Explain how a square is

 (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle 

4. Name the quadrilaterals whose diagonals. 

(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal 

5. Explain why a rectangle is a convex quadrilateral.

6. ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

Chapter 3: Ex 3.4 Understanding Quadrilaterals Free PDF

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