Triangle Congruence

1. Angle-Side-Angle (ASA)

1.1. Two pairs of congruent angles

1.2. One pair of congruent sides

1.2.1. The side must be shared by the two angles

2. Angle-Angle-Side (AAS)

2.1. Two pairs of congruent angles

2.2. One pair of congruent sides

2.2.1. The side must be opposite one of the angles

3. Angle-Side-Side (ASS)

3.1. DOES NOT GUARANTEE CONGRUENCE

3.2. One pair of congruent angles

3.2.1. The angle must be opposite one of the sides

3.3. Two pairs of congruent sides

3.4. Hypotenuse-Leg (HL)

3.4.1. DOES GUARANTEE CONGRUENCE

3.4.2. A special case of ASS where the angle is 90° (right triangle)

3.4.3. One pair of congruent hypotenuses

3.4.4. One pair of congruent legs

4. Side-Side-Side (SSS)

4.1. Three pairs of congruent sides

4.2. Leg-Leg (LL)

4.2.1. A special case of SSS

4.2.1.1. The third side can be found using the Pythagorean Theorem

4.2.2. Two pairs of congruent legs in a right triangle

5. Side-Angle-Side (SAS)

5.1. Two pairs of congruent sides

5.2. One pair of congruent angles

5.2.1. The angle must be formed by the two sides

5.3. Leg-Leg (LL)

5.3.1. A special case of SAS where the angle is 90°

5.3.2. Two pairs of congruent legs in a right triangle