Copying an angle and constructing a bisector

To construct the bisector of angle A: 1) draw a circle of any radius centred at A meeting the sides at B and C; 2) without changing the radius, draw circles centred at B and C and mark their intersection D; 3) draw ray AD. Justification: in △ABD and △ACD, AB = AC, BD = CD and AD is common, so they are equal by SSS and ∠BAD = ∠CAD. A right angle can also be divided into three equal parts (using the intersection points of circles centred at B and C with the first circle). It was proved later that an arbitrary angle cannot be trisected with compass and straightedge; for example, 60° cannot be divided into three equal parts.