Revision Exercise Symmetry (Including Constructions on Symmetry)
ICSE Class 6 · Mathematics · Chapter 30
What this chapter covers
- Symmetry around you
- Line of symmetry
- Lines of symmetry of common shapes
- Mirror images and reflection
- Constructions on symmetry
Key points
- Symmetry is the quality of a shape whose two halves match exactly when folded along a line.
- A line of symmetry is also called an axis of symmetry; a figure may have none, one, many or countless such lines.
- Scalene triangle 0, isosceles triangle 1, equilateral triangle 3, rectangle 2, rhombus 2, square 4 lines of symmetry.
- A regular polygon has as many lines of symmetry as sides; every diameter of a circle is a line of symmetry.
- The diagonals of a rectangle are not lines of symmetry unless the rectangle is a square.
- A mirror image has the same size and shape and the same distance from the mirror line, but left and right are swapped (lateral inversion).
- To reflect a point, draw a line from it at a right angle to the mirror line and mark the same distance on the other side.
- To reflect a figure, reflect each corner and join the images in the same order.
- The perpendicular bisector is the axis of symmetry of a line segment; the angle bisector is the axis of symmetry of an angle.
Questions answered
What is a line of symmetry?
A line of symmetry is a line that divides a figure into two parts that match exactly when the figure is folded along it.
How many lines of symmetry does a square have? Name them.
A square has four lines of symmetry: its two diagonals and the two lines that join the middles of opposite sides.
Is a diagonal of a rectangle a line of symmetry? Give a reason.
No. When a rectangle is folded along a diagonal, the corners stick out and the two halves do not match. Only a square, which is a special rectangle, has its diagonals as lines of symmetry.
Write three capital letters with no line of symmetry and two letters with two lines of symmetry.
No line of symmetry: F, J, S (also G, L, N, P, Q, R, Z). Two lines of symmetry: H and X (also I and O).
How many lines of symmetry does a regular octagon have? How many does a circle have?
A regular octagon has 8 lines of symmetry. A circle has countless lines of symmetry, because every diameter is one.
A point is 5 squares above a horizontal mirror line on squared paper. Where is its mirror image?
Its image is 5 squares below the mirror line, in the same column.
Why is the word AMBULANCE painted back to front on the front of the vehicle?
A mirror swaps left and right, which is called lateral inversion. A driver in front sees the word in the rear-view mirror the right way round.
Which construction gives the line of symmetry of a line segment, and which gives the line of symmetry of an angle?
The perpendicular bisector is the line of symmetry of a line segment. The angle bisector is the line of symmetry of an angle.