Geometry for Elementary School/Copying an angle

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Geometry for Elementary School
Copying a triangle Copying an angle Why the constructions are not correct?


In this chapter, we will show how to copy an angle \angle ABC to other angle \angle CDE. The construction is based on Book I, proposition 23.

[edit] The construction

  1. Draw a line between A and B and get \triangle ABC.
  2. Copy the triangle \triangle ABC and get \triangle CDE

[edit] Claim

The angles \angle ABC and \angle CDE are equal.

[edit] Proof

  1. The triangles \triangle ABC and \triangle CDE congruence.
  2. Therefore the angles of the triangles equal.
  3. Hence, \angle ABC and \angle CDE are equal.

Note that any two points on the rays can be used to create a triangle.

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