Instruction: Construct the line that bisects the given angle.
Goal: 2L 4E
- Perpendicular Bisector
Previous level: 1.7
Next level: 2.2
2L 4E solution
Let A be the vertex of the angle.
- Construct a circle C1 with center A and an arbitrary radius, intersecting the sides of the angle at B and C
- Construct the perpendicular bisector P1 of BC
The circle allows you to construct an arbitrary isosceles triangle ABC with BC as its base. Then, constructing the perpendicular bisector of its base also allows you to find the required angle bisector as in an isosceles triangle, the angle bisector from the apex coincides with the perpendicular bisector of its base.