Euclidea Wiki
Advertisement
BisectAngleDetailed.8a3113fa7c8c2c31c9555991bda860f8.png

Instruction: Construct the line that bisects the given angle.

Goal: 2L 4E

Available tools:

  • Move
  • Point
  • Line
  • Circle
  • Perpendicular Bisector
  • Intersect

Pack: Beta

Previous level: 1.7

Next level: 2.2

2L 4E solution[]

2.1-2L 4E.PNG

Let A be the vertex of the angle.

  1. Construct a circle C1 with center A and an arbitrary radius, intersecting the sides of the angle at B and C
  2. Construct the perpendicular bisector P1 of BC

Explanation[]

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.

Advertisement