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]

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!


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.