The congruence criteria answer a practical question: how many, and which, elements of a triangle must one know in order to determine it uniquely? Three “right” pieces of information are enough. The first criterion starts from two sides and the angle they include.
Theorem — First congruence criterion
If two triangles have respectively congruent two sides and the included angle, then the two triangles are congruent.
In the drawing, the equal marks on the sides and the arc on the angle indicate the congruent elements of the two triangles.
Two sides and the included angle congruent: the two triangles are congruent (first criterion, “side-angle-side”).
Links
Topics: Euclidean geometry
Concepts: Angle · Congruence · Congruence criteria · Triangle
Skills: Synthetic geometry