Postulate 12 (SSS Postulate)

If three sides of one triangles are congruent to three sides of another triangle, then the triangles are congruent.

Triangle ABC is congruent to Triangle DEF by SSS Postulate

Postulate 13 (SAS Postulate)

If Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Triangle ABC is Congruent to Triangle DEF by SAS Postulate

Postulate 14 (ASA Postulate)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangle are congruent.

Triangle ABC is Congruent to Triangle DEF by ASA Postulate

Theorem 4-1 (The Isosceles Triangle Theorem)

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Angle A is Congruent to Angle C by the Isosceles Triangle Theorem

Corollary 1

An equilateral triangle is also equiangular

Corollary 2

An equilateral triangle has three 60 degree angles

Corollary 3

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

Theorem 4-2

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Corollary

An equiangular triangle is also equilateral

Theorem 4-3 (AAS Theorem)

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Triangle ABC is congruent with triangle DEF by the AAS theorem

Theorem 4-4 (HL Theorem)

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Triangle ABC is Congruent with triangle DEF by the HL Theorem

Note: This theorem only applies to right triangles. The side opposite from the right triangle is called the hypotenuse. The other two sides are called legs.