It means that the angles have the same measure (for example, in degrees).
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'corresponding parts of congruent triangles are congruent'
Angle-Side-Angle is also called ASA. ASA formula is used to determine congruency. It means that 2 triangles are congruent if 2 angles and the included side of one triangle are congruent to 2 angles and the included side of the other triangle.
Angle Angle Side is a method one can use to prove that two triangles are congruent. Basically, if any two pairs of angles and the side between these angles are congruent, then the triangles are congruent as well.
Liney The same
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).