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

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Geometry for Elementary School
The Angle-Side-Angle congruence theorem The Side-Angle-Angle congruence theorem The Right angle-Hypotenuse-Side congruence theorem

In this chapter, we will discuss yet another congruence theorem, the Side-Angle-Angle congruence theorem, usually abbreviated as SAA.

The Angle-Side-Angle congruence theorem[edit]

Given two triangles \triangle ABC and \triangle DEF such that their sides are equal, hence:

  1. The angle \angle BAC equals \angle EDF .
  2. The angle \angle ABC equals \angle DEF .
  3. The side \overline {BC} equals \overline {EF} .

Then the triangles are congruent and their other angles and sides are equal too. Note that the side must be the included side of the two angles.