Constructions - Angle and Perpendicular Bisectors

A pair of compasses and a ruler only is to be used. After pupils get familiar in carrying out angle bisectors and perpendicular bisectors, they are challenged to apply those skills in finding the following specific angles: 60, 30, 45.

The most challenging exercise is to construct a perpendicular line to a given line and the perpendicular line must pass through a given point.

For example: a perpendicular line on line a segment AB, which is not horizontal, and from a point P above the line segment AB, is required to be constructed.

The following knowledge is required:

1. The angle bisector of an isosceles triangle can also become perpendicular bisector.

2. A line from the centre of circle to the midpoint of a chord forms 90 degrees.

3. The radius of a circle to a tangent to the circle will form 90 degrees at the point of contact.