Worksheet on Linear Symmetry

Practice the questions given in the worksheet on linear symmetry.The questions will help us to find whether the given figures possess  linear symmetry.

Review the linear symmetry & lines of symmetry and then solve the questions given in the worksheet on linear symmetry in different figures.

1. Write the number of lines of symmetry in the following figures.

(i) Equilateral triangle             

(ii) Isosceles triangle               

(iii) Scalene triangle

(iv) Square                              

(v) Rhombus                           

(vi) Rectangle

(vii) Parallelogram                  

(viii) Trapezium                                  

(ix) Circle                   

(x) Semi circle

2. Which letters of English alphabet possess

(i) Vertical line of symmetry               

(ii) Horizontal line of symmetry

(iii) Both Horizontal and Vertical line of symmetry    

(iv) No line of symmetry

(v) Infinite lines of symmetry

3. Construct the following figures and draw the lines of symmetry in them.

(i) ∆ XYZ such that XY = YZ = ZX = 5 cm    

(ii) ∆ ABC such that AB = BC = 3.5 cm and AC = 2 cm

(iii) Square PQRS of side 4 cm                               

(iv) Rectangle PQRS, PQ = 1.7 cm and QR = 3.8 cm

(v) ∠A = 45°, ∠B = 50° and AB = 3.5 cm

4. Draw the following polygons:

(i) Regular pentagon               

(ii) Regular hexagon               

(iii) Regular heptagon

(iv) Regular octagon

What can you say about the number of sides and number of lines of symmetry in each?

5. Draw a quadrilateral having the following lines of symmetry.

(i) 0     

(ii) 1    

(iii) 2   

(iv) 4

6. Draw a triangle having the following lines of symmetry.

(i) 0     

(ii) 1    

(iii) 2   

(iv) 3

7. What is other name you can give to the line of symmetry of the following:

(i) Isosceles triangle                

(ii) Circle                    

(iii) Rhombus

(iv) Line segment                    

(v) Angle                    

(vi) Equilateral triangle

8. Find the order of rotational symmetry in the following letters:

Worksheet on Linear Symmetry

9. Name any three geometrical figures that possess both lines of symmetry and rotational symmetry

10. Draw two figures that have no line of symmetry but possess rotational symmetry.

11. Draw two figures that possess line of symmetry but no rotational symmetry.

12. Name the figure which neither has line of symmetry nor rotational symmetry.

13. Where does the center of rotation for the following figure lie?

(i) circle

(ii) square

(iii) equilateral triangle

(iv) rectangle

14. Through what angle of rotation are the following figures rotated to find the order of rotation.

(i) Square

(ii) parallelogram

(iii) equilateral triangle

(iv) regular hexagon

(v) circle

15. Find the order of rotational symmetry in the following figures.

(i) Kite

(ii) Rhombus

(iii) Semicircle

(iv) Isosceles trapezium

(v) Isosceles triangle

(vi) Regular hexagon

(vii) Scalene triangle

Answers for the worksheet on linear symmetry are given below to check the exact answers of the above questions on symmetrical lines.


1. (i) 3

(ii) 1

(iii) 0

(iv) 4

(v) 2

(vi) 2

(vii) 0

(viii) 4

(ix) infinity

(x) 1

2. (i) A, H, I, M, O, T, U, V, W, X, Y               

(ii) B, C, D, E, H, I, K, O, X

(iii) H, I, O, X

(iv) F, G, J, L, N, P, Q, R, S, Z

(v) O

7. (i) bisector of the vertical angle

(ii) diameter          

(iii) diagonal

(iv) perpendicular bisector                     

(v) angular bisector                     

(vi) median

8. (i) 2

(ii) 2

(iii) infinity

(vi) 2

(v) 2

(vi) 2

(vii) none

9. Rectangle, rhombus, circle

12. Scalene triangle

13. (i) point of intersection of diameters

(ii) point of intersection of diagonals

(iii) centroid

(iv) point of intersection of diagonals

14. (i) 90°

(ii) 180°

(iii) 120°

(iv) 60°

(v) any angle

15. (i) none

(ii) 2

(iii) none

(iv) none

(v) none

(vi) 6

(vii) none

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