Congruence theorems

From true

Congruence is a term which modern geometers use but which was not part of Euclid's terminology. The easy was to introduce it into Euclid's system is to add it as a definition:

Definition 24: Two triangles ABC and DEF are congruent if the angles A, B, and C equal the angles D, E, and F respectively, and the sides AB, BC, and AC equal the sides DE, EF, and DF respectively, and the triangle ABC equals the triangle DEF (by which is meant that they have the same area). [1]

This definition can be summarized as, "If two triangles are congruent, their corresponding parts are equal and their areas are equal."

[edit] Side-Side-Side

If the corresponding sides of two triangles are equal, then the two triangles are congruent.

How would you prove this?

[edit] Side-Angle-Side

If two corresponding sides and the included angle of two triangles are equal, then the two triangles are congruent.

Proof?

[edit] Angle-Side-Angle

If two corresponding angles and the included side of two triangles are equal, then the two triangles are congruent.

Proof?