Geometry for Elementary School/Copying an angle

Geometry for Elementary School
Copying a triangle Copying an angle Constructing a triangle


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

The construction

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  1. Draw a line between A and C and get  .
  2. Copy the triangle   and get  

Claim

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The angles   and   are equal.

Proof

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  1. The triangles   and   congruence.
  2. Therefore the angles of the triangles equal.
  3. Hence,   and   are equal.

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