Symmetry

Symmetry is all around us, in leaves, butterflies, rangoli designs, buildings such as the Taj Mahal and many letters of the alphabet. A figure has line symmetry if it can be folded along a line so that its two parts coincide exactly. That fold line is called the line of symmetry or axis of symmetry. In this chapter you will make symmetric figures with ink-blots, paper folding and paper cut-outs, and identify the lines of symmetry of common shapes. You will find that some figures have no line of symmetry, some have exactly one, like an isosceles triangle or the letter A, and some have two, like a rectangle. The chapter then explores figures with many lines of symmetry. A square has 4, an equilateral triangle has 3, a regular hexagon has 6, and a circle has countless lines of symmetry. Finally, you will connect symmetry with reflection in a mirror, where the image is the same distance behind the mirror as the object is in front and left and right are interchanged.

Detailed Worksheet: Symmetry Section A - Definitions (10 marks) 1. What is meant by line symmetry? Give two examples from nature. (2 marks) 2. What is a line of symmetry? How can you check whether a line is a line of symmetry by paper folding? (2 marks) 3. What is a regular polygon? State the relation between the number of sides of a regular polygon and its lines of symmetry. (2 marks) 4. How is mirror reflection related to line symmetry? (2 marks) 5. Name a figure with no line of symmetry and a figure with infinitely many lines of symmetry. (2 marks) Section B - Calculations and Applications (15 marks) 6. Write the number of lines of symmetry of: (i) a square (ii) a rectangle (iii) an equilateral triangle (iv) a regular pentagon (v) a scalene triangle (vi) a circle. (3 marks) 7. Among the capital letters A, B, C, D, E, H, I, M, O, S, T, X and Z, list (i) letters with exactly one vertical line of symmetry (ii) letters with exactly one horizontal line of symmetry (iii) letters with no line of symmetry. (3 marks) 8. Find the total number of lines of symmetry in a set of figures made up of 2 squares, 3 equilateral triangles and 1 regular hexagon. Also find how many more lines a regular octagon has than a rectangle. (3 marks) 9. Which of the following figures have exactly two lines of symmetry: a rhombus, a kite, a rectangle, an isosceles trapezium, a parallelogram, the letter H? Give the count for each figure. (3 marks) 10. A word is written on a strip of paper and held in front of a mirror. Which of the words MOM, TOOT, HIDE and WOW will look exactly the same in the mirror? Explain your answer. (3 marks) Section C - Diagrams (10 marks) 11. Draw a square, a rectangle, an equilateral triangle and a regular hexagon, and draw all their lines of symmetry using dotted lines. Write the number of lines for each. (4 marks) 12. On squared paper, draw half of a figure on one side of a dotted vertical line (for example half a house shape) and complete it so that the dotted line is a line of symmetry. (3 marks) 13. Draw an isosceles triangle and a kite and show their lines of symmetry. State how many each has. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A student says, "Every quadrilateral has at least one line of symmetry." (i) Test this with a square, rectangle, rhombus, kite and a general parallelogram. (ii) Is the statement true? (iii) Draw a quadrilateral with no line of symmetry. (iv) Which quadrilateral has the most lines of symmetry? (5 marks) 15. Fold a sheet of paper twice to get four layers and cut out a design along the folded edges. (i) How many lines of symmetry will the opened design have at least? (ii) Why? (iii) How would the result change if the paper were folded three times along lines through one point to make 8 layers? (iv) Give one use of such designs in daily life. (5 marks) 16. Look at the digits 0 to 9 written in their usual printed form. (i) Which digits have a horizontal line of symmetry? (ii) Which have a vertical line of symmetry? (iii) Which have both? (iv) Write the largest three-digit number using only digits that look the same in a mirror held to the right of the number. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Draw lines of symmetry as dotted lines and use squared paper where asked.