A right triangle can have at most one line of symmetry.
If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.
If a rectangle has more than two lines of symmetry, then it must be a square.
With ruler and compasses, we can bisect any given line segment.
Only one perpendicular bisector can be drawn to a given line segment.
Two perpendiculars can be drawn to a given line from a point not lying on it.
With a given centre and a given radius, only one circle can be drawn.
Using only the two set-squares of the geometry box, an angle of 40° can be drawn.
Using only the two set-squares of the geometry box, an angle of 15° can be drawn.
If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.
A square and a rectangle have the same number of lines of symmetry.
A 45°-45°-90° set-square and a protractor have the same number of lines of symmetry.
It is possible to draw two bisectors of a given angle.
Infinitely many perpendiculars can be drawn to a given ray.
Infinitely many perpendicular bisectors can be drawn to a given ray.