Euclidea Wiki
Advertisement
DoubleAngleDetailed.073a6075b30cd2a7dc8841c82232fffd.png

Instruction: Construct an angle equal to the given one so that they share one side.

Goal: 3L 3E

Available tools:

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

Pack: Beta

Previous level: 2.3

Next level: 2.5

3L 3E solution[]

2.4-3L 3E.PNG

Let O be the vertex of the angle.

  1. Construct a circle C1 with an arbitrary center A on one ray and an arbitrary radius so that it intersects the other ray at least once. Let B be one of those intersections
  2. Construct a circle C2 with another arbitrary center C on the first ray and radius BC, intersecting circle C1 at D
  3. Construct line OD

Alternate 3L 3E solution:

2.4-3L 3E alternate.PNG

Let O be the vertex of the angle.

  1. Construct the circle C1 with center O and an arbitrary radius, intersecting the first ray at A and the second ray at B
  2. Construct a circle C2 with an arbitrary center C on the first ray and radius BC, intersecting circle C1 at D
  3. Construct line OD

2V solution[]

2.4-2V.PNG
  1. Construct a circle C3 with an arbitrary center E on the second ray and an arbitrary radius so that it intersects the first ray at least once. Let F be one of those intersections
  2. Construct a circle C4 with another arbitrary center G on the second ray and radius FG, intersecting circle C3 at H
  3. Construct line OH
2.4-2V alternate.PNG

From the alternate 3L 3E solution:

  1. Construct a circle C3 with an arbitrary center E on the second ray and radius AE, intersecting circle C1 at F
  2. Construct line OF

Explanation[]

The first circle allows you to pick any point on the other ray and the second circle allows you to create the reflection of that point through the first ray. Then by tracing the line OD, you're actually constructing the reflection of the second ray through the first ray, so it's angle to the first ray will be the same.

Advertisement