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Postulates on Proving Congruence of Triangles


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Angle Side Angle Postulate (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
Hypotenuse Leg Theorem (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent
Side Side Side Postulate (SSS)
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Side Angle Side Postulate (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
Angle Angle Side Postulate (AAS)
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the triangles are congruent