c Try a shape that does not have any corners or sides.
A
aExample Solution: an isosceles triangle.
B
bExample Solution: a rectangle.
C
cExample Solution: a circle.
Practice makes perfect
a A figure is said to have a line symmetry if there exists at least one line such that, if the figure is reflected in it, the preimage and image are identical. An example of a shape that has exactly one line of symmetry is an isosceles triangle.
The angles and lengths of the triangles the line divides the isosceles triangle into are congruent. When reflecting the shape along the line, the figure will therefore be identical.
b To find a shape that has exactly two lines of symmetry, let's consider a quadrilateral.
It has two lines of symmetry. They both go through the midpoint and are parallel to the sides.
Note that if we'd chosen a square, the diagonals would also be lines of symmetry, and it would have four lines of symmetry in total.
c By looking at the first exercises it seems that the number of sides and corners have an impact on the number of lines of symmetry. What about a shape that has no corners or sides: a circle?
Here, any line through the midpoint of the circle is a line of symmetry. Since there are infinitely many lines that do that, a circle has infinitely many lines of symmetry.
