Each of our Ganita Prakash Class 6 Worksheet and Class 6 Maths Chapter 9 Symmetry Worksheet with Answers Pdf focuses on conceptual clarity.
Class 6 Maths Chapter 9 Symmetry Worksheet with Answers Pdf
Symmetry Class 6 Maths Worksheet
Class 6 Maths Chapter 9 Worksheet with Answers – Class 6 Symmetry Worksheet
A. Choose the correct option.
Question 1.
In. the following figures, the figure that is not symmetric with respect to any Line S:
Answer:
(b)
Question 2.
An isosceles triangle has
(a) rotational symmetry of order 1
(b) line symmetry
(c) rotational symmetry of order more than 1
(d) Both (a) and (b)
Answer:
(d) Both (a) and (b)
Question 3.
Which of the following have both rotational symmetry and line of symmetry?
(a) A square
(b) A circle
(c) An equilateral triangle
(d) All of these
Answer:
(d) All of these
Question 4.
A circle has:
(a) zero line of symmetry
(b) 1 line of symmetry
(c) 2 lines of symmetry
(d) infinite lines of symmetry
Answer:
(d) infinite lines of symmetry
Question 5.
The number of lines of symmetry in a pair of compasses is
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0
Question 6.
Which of the following alphabets have vertical and horizontal line of symmetry?
(a) A
(b) H
(c) B
(d) M
Answer:
(b) H
Question 7.
Which of the following have only one line of symmetry?
(a) A rhombus
(b) A scalene triangle
(c) An isosceles triangle
(d) A rectangle
Answer:
(c) An isosceles triangle
Question 8.
Order of rotational symmetry of a hexagon is
(a) 2
(b) 3
(c) 4
(d) 6
Answer:
(d) 6
Directions.: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Question 9.
Assertion (A): This figure has no line of symmetry.
Reason (R): The line of symmetry is a line that divides an object into two identical pieces.
Answer:
(d) Assertion (A) is false but Reason (R) is true.
Question 10.
Assertion (A):
Reason (R): The angle of symmetry of the given figure is 180°.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B. Fill in the blanks.
1. In an isosceles right triangle, the number of lines of symmetry is _______
Answer:
1
2. If a line segment of length 12 cm is reflected in the line of symmetry (mirror), then its reflection (image) is a line segment of length _______
Answer:
12 cm
3. Angle of rotational symmetry of a semicircle is _______
Answer:
360°
4. Arrowhead has _______ line(s) of symmetry.
Answer:
1
5. Order of rational symmetric of
is _______
Answer:
8
C. Solve the following.
Question 1.
Draw the second half of each symmetrical letter.
Question 2.
Give the order of rotational symmetry for the given figure:
Answer:
6
Question 3.
By what minimum angle do a rectangle and a regular pentagon rotate to coincide with their original position for the first time?
______________________________________
Answer:
180°; 72°
Question 4.
Give an example of any two English alphabets that have rotational symmetry of order 2. Show their rotational symmetry also.
______________________________________
Answer:
(a) BOOK, BED (answer may vary)
(b) WOW, MOM (answer may vary)
Question 5.
(a) Write at least two words other than the word ‘CHOICE’ that have horizontal lines of symmetry.
______________________________________
(b) Write at least two words other than the word ‘MAM’ that have vertical lines of symmetry.
______________________________________
Question 6.
Complete the given figure so that l is the line of symmetry of the completed figure.
HOTS Question
Draw the reflected image for the word Mathematics.
Maya and Anuj are making some decorative items by paper folding and cutting for the decoration of their home on Diwali.
Maya: Hey Anuj! How do you make this beautiful design?
Anuj: It is called a symmetrical paper cut design.
Maya: Okay! I know about the concept of symmetry. We can see symmetry everywhere, in nature and also in many architectural structures.
Anuj: Yes! ‘Symmetry’ refers to the exact match in shape and size between two halves of an object.
Maya: Yes, you are right. A line about which a figure is symmetrical is called the line of symmetry or axis oj symmetry.
Question 1.
Here are some pictures of natural as well as man-made things. Can you Identify whether they are symmetrical or not? Write them. If they have, then draw their line of symmetry.
Ariuj: Lines of symmetry can be horizontal, vertical, and diagonal. Some shapes or objects have multiple lines of symmetry.
Question 2.
Draw line (s) of symmetry for the following objects and write how many lines they have.
Answer:
(a) 1
(b) 1
(c) 5
(d) 4
(e) 8
(f) 2
Question 3.
Name any four figures or shapes which have only 2 lines of symmetry.
Answer:
Rectangle, rhombus, oval, letter H (Answer may vary)
LINE OF SYMMETRY FOR GEOMETRICAL FIGURES
Question 4.
Draw the line(s) of symmetry for the following geometric shapes and complete the given statements.
Answer:
(a) 1
(b) 1
(c) 3
(d) 2
(e) 4
(f) infinite
Think and Answer
Which triangle does not have any line of symmetry? Why?
Answer:
(a)
Question 5.
Draw as many lines of symmetry as possible in each of the following figure.
Activity
Take an A4 sheet of paper and fold it into two equal halves. Draw any geometric shapes along one part of the fold and cut it out using a scissors. Now, open the fold and observe. What shape will you get? Is the shape symmetrical about the crease formed?
REFLECTION SYMMETRY
Reflection symmetry is a type of symmetry that occurs, when a figure or object is reflected across a line, that gives two proportional, equal-sized and equal-shape parts. This line is also known as line symmetry or mirror symmetry. This line can be in any direction.
Question 6.
Complete the following figures in such a way that the completed figure is symmetric about the given dotted line (line of symmetry).
Question 7.
Complete the following figures using the mirror Line symmetry.
Fun Time
Complete the shape that satisfies the line of symmetry.
Question 8.
Complete each of the following figures along the axes (Lines of symmetry).
PUNCHING GAME
Using a punching machine, punch holes at different locations of a folded sheet of paper to create different symmetric patterns.
Question 9.
Along the given line(s) of s9mmetry, find the other hole(s) in the following figures.
Question 10.
Find the line (s) of symmetry of the following figures with punched holes.
ROTATIONAL SYMMETRY
Raman and Sameer are friends. They are playing with afidget spinner.
Raman.: Hey! It looks similar while we rotating about its centre.
Sameer: Yes, because it has rotational symmetry.
A figure has rotational symmetry when it can be rotated less than a full rotation clockwise or counterclockwise about a fixed point to a position in which it looks the same as it does in its original position.
The angle through which a figure can be rotated to look exactly the same. It is called an angle of rotational symmetry or the angle of symmetry of the figure.
A figure or object that has an angle of symmetry strictly between 0 and 360 degrees is said to have rotational symmetry.
The point of the figure about which the rotation occurs is called the centre of rotation.
A figure or object may have multiple angles of symmetry.
Question 11.
The given figure is rotated about its centre of rotation in a clockwise direction. Mark the dot (•) as given in the original figure in all its rotating positions according to the angles of rotation.
After giving _______ turns of clockwise rotation of _______, we get the original position of the figure. So, the order of rotational symmetry of the given figure is _______
Answer:
4; 90°; 4
Question 12.
Observe the rotational symmetry of an equilateral triangle and write the angle of rotation for each turn.
Answer:
120°, 120°, 120”
Question 13.
Find the order of angles of symmetry for the given figures about the point marked (.).
Answer:
(a) 4
(b) 2
(c) 4
Think and Answer
What do you think about the rotational symmetry of zero ‘0’ and letter ‘O’? How many orders of rational symmetry do they have?
Answer:
Order of rotational symmetry of 0 = 2,
Order of rotational symmetry of O = 2
Question 14.
After rotating by 40° around a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer:
80°, 120°, 160”, 200”, 240”, 280″, 320”, 360“
Question 15.
Many objects or shapes have both lines and rotational symmetry. Complete the given table.
Answer:
27
Think and Answer
Redraw the following diagram using a pair of compasses. And then draw line (s) of symmetry on the drawn figure. Does the figure have rotational symmetry? If yes, then find the angle of rotation and order of rotational symmetry.
