Geometry for Elementary School/The Side-Angle-Side congruence theorem

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Geometry for Elementary School
The Side-Side-Side congruence theorem The Side-Angle-Side congruence theorem The Angle-Side-Angle congruence theorem

In this chapter, we will discuss another congruence theorem, this time the Side-Angle-Side theorem. The angle is called the included angle.

The Side-Angle-Side congruence theorem[edit | edit source]

Given two triangles and such that their sides are equal, hence:

  1. The side equals .
  2. The side equals .
  3. The angle equals (These are the angles between the sides).

Then the triangles are congruent and their other angles and sides are equal too. Success!

Proof[edit | edit source]

We will use the method of superposition – we will move one triangle to the other one and we will show that they coincide. We won’t use the construction we learnt to copy a line or a segment but we will move the triangle as whole.