Samacheer Kalvi Class 6 Maths Solutions Term 3 Chapter 4 Symmetry Exercise 4.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Symmetry Ex 4.1

Question 1. Fill in the blanks
(i) The reflected image of the letter 'q' is .......
(ii) A rhombus has lines of symmetry.
(iii) The order of rotational symmetry of the letter 'Z' is ..........
(iv) A figure is said to have rotational symmetry, if the order of rotation is atleast
(v) ......... symmetry occurs when an object slides to new position.
Answer:
(i) The reflected image of the letter 'q' is P.
(ii) A rhombus has two lines of symmetry.
(iii) The order of rotational symmetry of the letter 'Z' is 2.
(iv) A figure is said to have rotational symmetry, if the order of rotation is at least two.
(v) Translation symmetry occurs when an object slides to a new position. This means the figure moves without turning or flipping.
In simple words: The answers fill in the missing words for facts about mirror images, shapes, and movement in symmetry. For instance, 'q' seen in a mirror looks like 'P'.

🎯 Exam Tip: Understand the basic definitions of reflection, rotational, and translation symmetry to easily fill in these types of blanks.

Question 2. Say True or False
(i) A rectangle has four lines of symmetry.
(ii) A shape has reflection symmetry if it has a line of symmetry.
(iii) The reflection of the name RANI is INAЯ.
(iv) Order of rotation of a circle is infinite.
(v) The number 191 has rotational symmetry.
Answer:
(i) False. A rectangle has only two lines of symmetry, one horizontal and one vertical.
(ii) True. Reflection symmetry means a shape can be divided by a line so that both halves are mirror images.
(iii) False. The reflection of RANI would be INAЯ, but the R is also reversed to Я, so it should be INAЯ (or a similar reflection of R).
(iv) True. A circle looks exactly the same no matter how much you rotate it around its center, so it has endless rotational symmetry.
(v) False. The number 191 does not have rotational symmetry because it does not look the same after a 180-degree rotation.
In simple words: Check if each statement about symmetry is correct. For a circle, it can spin forever and always look the same.

🎯 Exam Tip: Visualize each statement carefully. For reflection, imagine a mirror. For rotation, imagine turning the object.

Question 3. Match the following shapes with their number of lines of symmetry.
i) Square
ii) Parallelogram
iii) Isosceles triangle
a) No line of symmetry
b) One line of symmetry
c) Two lines of symmetry
Answer:
(i) d (Square has 4 lines of symmetry, which is a common answer not listed in options a, b, c; however, the OCR solution maps it to 'd', implying 'd' represents 'Four lines of symmetry' from a missing option)
(ii) a (A parallelogram has no line of symmetry.)
(iii) b (An isosceles triangle has one line of symmetry.)
(iv) c (This part is from a missing question, but assuming it refers to a shape like a rectangle or rhombus for 'Two lines of symmetry' from option 'c').
In simple words: We are matching shapes to how many lines of symmetry they have. A line of symmetry is where you can fold a shape and both sides match perfectly.

🎯 Exam Tip: Remember the basic properties of common geometric shapes, especially their lines of symmetry and rotational symmetry.

Question 4. Draw the lines of symmetry of the following.
(i)
(ii)
(iii)
(iv)
Answer: (Visual solution requiring drawing lines of symmetry on the figures.) The solution involves identifying and drawing all possible lines through each given figure that divide it into two mirror-image halves.
In simple words: For each shape, you need to draw lines where you could fold the shape and have both halves look exactly the same.

🎯 Exam Tip: To find lines of symmetry, imagine folding the figure. Any fold line that makes the two halves match perfectly is a line of symmetry.

Question 5. Using the given horizontal line/ vertical line as a line of symmetry, complete each alphabet to discover the hidden word.
Answer:
(i) DECODE
(ii) KICK
(iii) BED
(iv) WAY
(v) MATY
(vi) TOMATO
In simple words: By drawing the mirror image of the half-letters shown, you complete them to form full letters, and then these letters spell out hidden words. This helps us see how symmetry works in letters.

🎯 Exam Tip: Pay close attention to the placement of the symmetry line (horizontal or vertical) when completing the letters. Each completed letter should be perfectly symmetrical across that line.

Question 6. Draw a line of symmetry of the given figures such that one hole coincides with the other hole(s) to make pairs.
Answer: (Visual solution requiring drawing lines of symmetry on the figures.) The solution involves drawing a line through each figure such that if folded along this line, the holes on one side perfectly overlap with the holes on the other side. This creates symmetrical pairs of holes.
In simple words: Draw a line through each picture so that if you folded it on that line, the holes would line up perfectly on top of each other.

🎯 Exam Tip: When dealing with multiple symmetrical points like holes, the line of symmetry must ensure that every point on one side has a corresponding mirror point on the other.

Question 7. Complete the other half of the following figures such that the dotted line is the line of symmetry.
Answer: (Visual solution requiring completing the figures.) The solution shows the completed figures, where the missing half is drawn as a perfect mirror image of the existing half, using the dotted line as the axis of symmetry. For instance, if half a heart is shown, the other half is drawn to complete it.
In simple words: Look at the dotted line in each picture. Then, draw the missing half of the shape exactly as it would appear if the dotted line were a mirror.

🎯 Exam Tip: Imagine reflecting the visible part of the figure across the dotted line. Every point on the original half should have a corresponding point at the same distance on the opposite side of the line.

Question 8. Find the order of rotation for each of the following.
Answer:
(i) 2 (For the letter H, it looks the same twice in a full 360-degree rotation.)
(ii) 2 (For the number 8, it looks the same twice in a full 360-degree rotation.)
(iii) 4 (For the cross-like shape, it looks the same four times as it turns.)
(iv) 8 (For the star-like figure with many points, it looks the same eight times.)
(v) 2 (For the two arrows pointing opposite, it looks the same twice in a full turn.)
In simple words: The order of rotation means how many times a shape looks exactly the same when you turn it a full circle (360 degrees).

🎯 Exam Tip: To find the order of rotational symmetry, mentally rotate the figure and count how many times it perfectly overlaps with its original position before completing a full 360-degree turn.

Question 9. A standard die has six faces which are shown below. Find the order of rotational symmetry of each face of a die?
Answer:
(i) 4 (For the face with one dot, the order of rotational symmetry is 4, considering the square shape of the face.)
(ii) 2 (For the face with two dots, the order of rotational symmetry is 2, as it aligns twice.)
(iii) 2 (For the face with three dots, the order of rotational symmetry is 2.)
(v) 4 (For the face with five dots, arranged in a square pattern, the order of rotational symmetry is 4.)
(vi) 2 (For the face with six dots, arranged in two rows of three, the order of rotational symmetry is 2.)
In simple words: We are checking how many times each face of a die looks the same when you rotate it in a full circle. For example, a face with one dot will look the same four times if you rotate the square face.

🎯 Exam Tip: When determining rotational symmetry for a die face, consider both the arrangement of the dots and the square shape of the face itself.

Question 10. What pattern is translated in the given border kolams?
Answer: (Visual solution identifying the translated pattern.) The solution indicates the repeating unit of the design, which is then copied and shifted to create the continuous border pattern. For example, for a string of 'H's, the 'H' itself is the translated pattern.
In simple words: Find the small part of the design that repeats over and over again to make the whole long pattern. That small part is the "translated pattern."

🎯 Exam Tip: Look for the smallest repeating segment that, if slid along the line, recreates the entire pattern. This segment is the unit of translation.

Question 11. Which of the following letter does not have a line of symmetry?
(a) A
(b) P
(c) T
(d) U
Answer: (b) P
In simple words: If you try to draw a line through the letter 'P' to make two mirror halves, you cannot. Letters A, T, and U can all be divided symmetrically.

🎯 Exam Tip: Imagine folding each letter. If you can't fold it perfectly in half so both sides match, it doesn't have a line of symmetry.

Question 12. Which of the following is a symmetrical figure?
(a) Figure A
(b) Figure B
(c) Figure C
(d) Figure D
Answer: (c) Figure C
In simple words: Only Figure C can be divided into two halves that are exact mirror images of each other, either horizontally or vertically. The other figures do not have this property.

🎯 Exam Tip: To check for symmetry, mentally draw lines through the center of the figure, both horizontally and vertically, to see if the parts on either side are identical.

Question 13. Which word has a vertical line of symmetry?
(a) DAD
(b) NUN
(c) MAM
(d) EVE
Answer: (c) MAM
In simple words: For a word to have vertical symmetry, each letter in the word must have vertical symmetry, and the overall word must also be symmetrical when cut down the middle. In MAM, both M and A have vertical lines of symmetry.

🎯 Exam Tip: To determine if a word has vertical symmetry, check each letter individually. Letters like M, A, H, I, T, U, V, W, X, Y, O have vertical symmetry. Letters like D, N, E do not.

Question 14. The order of rotational symmetry of 818 is .........
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
In simple words: If you rotate the number 818 by 180 degrees (half a turn), it will look exactly the same. Since it aligns with itself twice in a full circle, its rotational symmetry order is 2.

🎯 Exam Tip: The order of rotational symmetry is 1 if a figure only looks the same after a full 360-degree rotation. Any order greater than 1 means it aligns multiple times.

Question 15. The order of rotational symmetry ★ is ___
(a) 5
(c) 7
(d) 8
Answer: (a) 5
In simple words: A regular five-pointed star has an order of rotational symmetry of 5. This means you can turn it five times within a full circle (360 degrees), and it will look exactly the same each time. Each turn is 360/5 = 72 degrees.

🎯 Exam Tip: For regular polygons or star shapes, the order of rotational symmetry is usually equal to the number of sides or points they have.