1Draw these triangles on graph paper and draw their lines of symmetry: (a) an isosceles triangle standing on its base, (b) a taller isosceles triangle, (c) a right angled triangle with three unequal sides, (d) an isosceles triangle lying on its side with its apex pointing left.
2Draw the line or lines of symmetry of each of these figures: (a) an isosceles trapezium, (b) a bent arrow with a head at both ends, (c) a regular pentagon, (d) an arrow with a head at one end, (e) a heart shape, (f) a semicircular arch.
3Half of a figure is drawn on squared paper with a dotted line beside it. Taking the dotted line as the axis of symmetry, complete the figure. Explain how this is done.
4Make a list of the capital English letters that have linear symmetry and those that do not.
5Complete this table: how many lines of symmetry do an isosceles triangle, a square, a rectangle and an equilateral triangle have, and where do they lie?
6Decide whether each of these road signs has symmetry: (a) a circular no parking sign crossed by one slanting bar, (b) a triangular warning sign with circular arrows inside, (c) a blue circular sign with an arrow pointing down and to the left, (d) a blue rectangular sign with three slanting stripes.
7A hexagon has a square and a triangle drawn inside it. Is this a symmetric figure, and why?
8Find which shape is used in each pattern and how many there are: (a) a grid of coloured squares, (b) rectangles laid like bricks, (c) triangles alternating point up and point down, (d) a pattern made of hexagons.
9Using the dots given, make a rectangular tessellation and colour it suitably. How is it made?
10Using the dots given, make a square tessellation and colour it suitably. How does it differ from a rectangular one?
11From the things you have seen or own, find ten objects that have symmetry and ten that do not.
12The diagonal of a rectangle divides it into two parts of equal area. Is that diagonal a line of symmetry? Give the reason.
13Why do circles not form a tessellation?
14A square tessellation has 9 squares in a row and 7 such rows. How many squares are there in all? If the colours alternate between blue and white, how many squares of each colour are there?
15Half of a figure drawn on squared paper covers 11 small squares. When it is completed across the axis of symmetry, how many squares does the whole figure cover?
16In a brick wall each row is shifted half a brick along from the row below. Is this a tessellation? Give the reason.