107
Line symmetry
Textbook: Part 3, lesson 107, pp. 117–119
GoalLine symmetry: the axis of symmetry; symmetrical shapes; drawing the other half of a shape.
New words
symmetry · simmetriyaaxis of symmetry · simmetriya o‘qito coincide · ustma-ust tushmoqto reflect · akslantirmoq
Explanation
If one half of a shape, folded along a line, coincides exactly with the other half, the shape is symmetrical and the line is an axis of symmetry. A square has 4 axes (2 diagonals and 2 midlines), a rectangle that is not a square has 2, an isosceles triangle 1, an equilateral triangle 3. Every diameter of a circle is an axis of symmetry. To draw the other half of a shape, measure each vertex’s distance from the axis and put its mirror point the same distance on the other side. Among letters, A, T, M, H, O, X, Y, U, I have axes of symmetry.
Worked examples
The letter H has 2 axes: vertical and horizontal. A has one – the vertical. F has none.
If the left half of a symmetrical shape is 12 squares, the whole shape is 12 × 2 = 24 squares.
Class activity
“Fold and cut”: children fold paper, draw half a heart or tree against the fold, cut it out and, on opening, show the axis of the symmetrical shape.
Practice
1
How many axes of symmetry does a square have?
4
2
How many axes of symmetry does a rectangle that is not a square have?
2
3
How many axes of symmetry does an equilateral triangle have?
3
4
How many of the letters Q, A, M, S, O, T, F have at least one axis of symmetry?
4
5
A symmetrical stained-glass window uses 100 red, 60 green and twice as many blue pieces as green. How many pieces of glass are there in all?
280