Symmetry (Copy)
1.
Draw an isosceles triangle. Mark clearly its line of symmetry and write down its order of rotational symmetry.
2.
A square is drawn.
(a) Draw and label all its lines of symmetry.
(b) State its order of rotational symmetry.
3.
A rectangle has sides 6 cm and 4 cm.
(a) Draw all lines of symmetry.
(b) State its rotational symmetry order.
4.
An equilateral triangle has side 5 cm.
(a) Draw and mark all lines of symmetry.
(b) State its order of rotational symmetry.
5.
A regular pentagon is drawn.
(a) How many lines of symmetry does it have?
(b) What is its rotational symmetry order?
6.
A rhombus with diagonals 6 cm and 8 cm is drawn.
(a) Mark its lines of symmetry.
(b) State its rotational symmetry order.
7.
A parallelogram has sides 5 cm and 8 cm.
(a) State the number of lines of symmetry.
(b) State its rotational symmetry order.
8.
Draw a regular hexagon.
(a) Show all lines of symmetry.
(b) Write its rotational symmetry order.
9.
A kite is drawn.
(a) Mark its line of symmetry.
(b) State its order of rotational symmetry.
10.
A trapezium is drawn.
(a) State which type of trapezium has exactly one line of symmetry.
(b) State which type has none.
11.
The letter S is drawn.
(a) State its number of lines of symmetry.
(b) State its order of rotational symmetry.
12.
The letter O is drawn.
(a) How many lines of symmetry does it have?
(b) State its order of rotational symmetry.
13.
Draw a regular octagon.
(a) Show all lines of symmetry.
(b) Write its order of rotational symmetry.
14.
A cube is shown.
(a) State the number of planes of symmetry.
(b) State one axis of rotational symmetry and its order.
15.
A cuboid has dimensions 3 cm × 4 cm × 6 cm.
State how many planes of symmetry it has.
16.
A cylinder is drawn.
(a) State the number of planes of symmetry.
(b) Write the order of rotational symmetry about its axis.
17.
A cone is shown.
(a) State the number of planes of symmetry.
(b) State its order of rotational symmetry.
18.
A sphere is given.
(a) State the number of planes of symmetry.
(b) State its order of rotational symmetry.
19.
A triangular prism is given. Its base is an equilateral triangle.
(a) How many planes of symmetry does it have?
(b) What is its order of rotational symmetry about the axis of the prism?
20.
A square-based pyramid is drawn.
(a) How many planes of symmetry does it have?
(b) What is its order of rotational symmetry about the vertical axis?
21.
Draw an equilateral triangle and a scalene triangle side by side.
Compare their number of lines of symmetry and their orders of rotational symmetry.
22.
A rectangle is drawn and its diagonals are shown.
Explain how this relates to the rectangle’s symmetry.
23.
A rhombus and a kite are drawn.
(a) State which diagonals act as lines of symmetry.
(b) Compare their rotational symmetries.
24.
Which quadrilaterals have rotational symmetry of order 2?
Give two examples and justify.
25.
A regular dodecagon (12 sides) is drawn.
(a) State the number of lines of symmetry.
(b) State its order of rotational symmetry.
26.
The letter Z is drawn.
(a) State its number of lines of symmetry.
(b) State its order of rotational symmetry.
27.
The letter N is drawn.
(a) State its line of symmetry, if any.
(b) State its rotational symmetry order.
28.
Draw a circle.
(a) State the number of lines of symmetry.
(b) State its order of rotational symmetry.
29.
Which solids have infinite planes of symmetry?
Give two examples.
30.
A prism has a regular hexagonal base.
(a) State the number of planes of symmetry.
(b) State its order of rotational symmetry about its axis.
1.
Line of symmetry: vertical through apex and midpoint of base.
Rotational symmetry: order 1 (only maps at 360°).
2.
(a) 4 lines: two diagonals, vertical, horizontal.
(b) Rotational symmetry: order 4.
3.
(a) 2 lines: vertical through midpoint of shorter sides, horizontal through midpoint of longer sides.
(b) Rotational symmetry: order 2.
4.
(a) 3 lines, each through a vertex and opposite side midpoint.
(b) Rotational symmetry: order 3.
5.
(a) 5 lines of symmetry.
(b) Rotational symmetry: order 5.
6.
(a) 2 lines: along both diagonals.
(b) Rotational symmetry: order 2.
7.
(a) No line of symmetry.
(b) Rotational symmetry: order 2 (half-turn gives same shape).
8.
(a) 6 lines of symmetry (3 through opposite vertices, 3 through midpoints of opposite sides).
(b) Rotational symmetry: order 6.
9.
(a) 1 line: through the longer diagonal.
(b) Rotational symmetry: order 1.
10.
(a) Isosceles trapezium → 1 line (vertical through midpoints).
(b) Scalene trapezium → none.
11.
(a) No line of symmetry.
(b) Rotational symmetry: order 2 (turn 180° gives same).
12.
(a) Infinite lines (any diameter).
(b) Infinite order (every rotation maps).
13.
(a) 8 lines: 4 through opposite vertices, 4 through midpoints of opposite sides.
(b) Rotational symmetry: order 8.
14.
(a) 9 planes of symmetry.
(b) Examples: axis through opposite faces → order 4.
15.
3 planes of symmetry (through midpoints of opposite faces).
16.
(a) Infinite planes of symmetry (any plane through axis).
(b) Infinite order (rotation about axis works at any angle).
17.
(a) Infinite planes of symmetry (all planes through axis).
(b) Infinite order (about axis).
18.
(a) Infinite planes of symmetry.
(b) Infinite order of rotational symmetry.
19.
(a) 3 planes: each through axis and one altitude of triangular base.
(b) Rotational symmetry: order 3 about prism axis.
20.
(a) 4 planes: each through axis and midpoint of opposite sides of base.
(b) Order 4 about vertical axis.
21.
Equilateral triangle → 3 lines, order 3.
Scalene triangle → none, order 1.
22.
Rectangle diagonals are not lines of symmetry (only in a square). They cross at centre but do not divide into mirror halves.
23.
Rhombus → both diagonals are lines of symmetry.
Kite → only the diagonal connecting unequal sides is a line of symmetry.
Rotational symmetry: rhombus order 2, kite order 1.
24.
Order 2 quadrilaterals: rectangle, rhombus, parallelogram.
25.
(a) 12 lines.
(b) Order 12.
26.
(a) No line.
(b) Rotational symmetry order 2 (180° rotation works).
27.
(a) No true line of symmetry.
(b) Rotational symmetry: order 2 (180° rotation gives same).
28.
(a) Infinite lines of symmetry.
(b) Infinite order rotational symmetry.
29.
Solids with infinite planes: sphere, cylinder, cone.
30.
(a) 6 planes (like base symmetry extended through prism).
(b) Order 6 about its axis.