Congruent-why such a funny word that basically means equal? Probably because they are only equal when laid on top of each other. Anyway it comes from Latin congruere, to agree. So the angles agree.
https://www.mathsisfun.com/geometry/congruent-angles.html
SAS (Side-Angle-Side). A second way to prove the congruence of triangles is to show that two sides and their included angle are congruent. This method is called side-angle-side. It is important to remember that the angle must be the included angle--otherwise you can't be sure of congruence.
http://www.sparknotes.com/math/geometry2/congruence/section2.rhtml
Corresponding Angles Postulate. If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent. Converse also true: If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel. The figure above yields four pairs of corresponding angles.
https://www.wyzant.com/resources/lessons/math/geometry/lines_and_angles/angle_theorems
Congruent Angles have the same angle (in degrees or radians). These angles are congruent. They don't have to point in the same direction. They don't have to be on similar sized lines.
https://www.mathsisfun.com/geometry/congruent-angles.html
Angles are congruent if they have the same angle measure in degrees. They can be at any orientation on the plane. In the figure above, there are two congruent angles. Note they are pointing in different directions. If you drag any of the endpoints, the other angle will change to remain congruent with the one you are changing. For angles, 'congruent' is similar to saying 'equals'.
http://www.mathopenref.com/congruentangles.html
When two sides of a triangle and the angle between them are the same as the corresponding parts of another triangle there is no way that the triangles aren't congruent. When two sides and their included angle are fixed, all three vertices of the triangle are fixed.
http://www.sparknotes.com/math/geometry2/congruence/section2.rhtml
ASA (Angle-Side-Angle). The third major way to prove congruence between triangles is called ASA, for angle-side-angle. If two angles of a triangle and their included side are congruent, then the pair of triangles is congruent.
http://www.sparknotes.com/math/geometry2/congruence/section2.rhtml
Angles are congruent if their measures, in degrees, are equal. Note : congruent does not mean equal.. While they seem quite similar, congruent angles do not have to point in the same direction. The only way to get equal angles is by piling two angles of equal measure on top of each other.
https://www.wyzant.com/resources/lessons/math/geometry/lines_and_angles/angle_theorems
If a transversal intersects two parallel lines, then the alternate interior angles are congruent. Converse also true: If a transversal intersects two lines and the alternate interior angles are congruent, then the lines are parallel.
https://www.wyzant.com/resources/lessons/math/geometry/lines_and_angles/angle_theorems
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short. To use it, you must know the lengths of all three sides of both triangles, or at least know that they are equal.
http://www.sparknotes.com/math/geometry2/congruence/section2.rhtml
when two angles are congruent
When two angles have the same angle measure in degrees it is said to be congruent. Two angles are congruent, if they have the same angle measure in degrees.