Question

congruences of triangles

Answer 1

Two triangles are congruent implies that all the angles measure the same and all the sides are equal.  This also means that all the properties related to other aspects of the triangles will be same. like lengths of medians, perpendiculars, centroid etc.

When two sides and the angle between them in one triangle are equal to two sides and their angle between them - they are congruent.

When all sides are equal then the triangles will be congruent. When all angles are equal then they are similar. When all angles are equal and one side is the same between two triangles, then they r congruent.

Answer 2

Two triangles are congruent if they are copies of each other and when superposed, they cover each other exactly.
SSS congruence criterion:
If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
SAS congruence criterion:
If under a correspondence, two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.
ASA congruence criterion:
If under a correspondence, two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle, then the triangles are congruent.
RHS congruence criterion:
If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of the another right angled triangle, then the angles are congruent.