Triangle Congruence
by Nick Elsbury
1. Angle Angle Side (AAS)
1.1. If triangle ABC and triangle DEF are two triangles such that angle ABC is congruent to angle DEF, angle BCA is congruent to angle EFD, and AC is congruent to DF, then triangle ABC is congruent to triangle DEF.
2. Hypotenuse Leg Theorem
2.1. If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
3. Two triangles are congruent by Side Angle Side. (SAS)
3.1. If triangle ABC and triangle DEF are two triangles such that AB = DE, angle ABC = angle DEF, and BC = EF, then triangle ABC is congruent to triangle DEF.
4. Side Side Side (SSS)
4.1. If triangle ABC and triangle DEF are two triangles such that segment AB = segment DE, segment BC = segment EF, and segment CA = segment FD, then triangle ABC is congruent to triangle DEF.
5. Angle-Side Angle (ASA)
5.1. If triangle ABC and triangle DEF are two triangles such that angle CAB is congruent angle FDE, segment AB is congruent to segment DE, and angle ABC is congruent to angle DEF, then triangle ABC is congruent to triangle DEF.
6. Each side on one triangle is equal to other side on a different triangle
7. Each side on one triangle is equal to other side on a different triangle
8. If two triangle are congruent then they are similar
8.1. Ex. If triangle ABC and triangle DEF are two congruent triangles then triangle ABC is also similar to triangle DEF
