Theory:

With superposition principle, we match the corresponding sides, vertices, and angles to know whether the two given triangles are congruent or not.
 
But, is it possible to construct congruent triangles?
 
Yes, it is possible construct congruent triangles with a few of the measurements known.
 
The three of the measurements are:
1. All three sides of the triangle known.
 
(or)
 
2. Any two sides and the angle between the sides known.
 
(or)
 
3. Any two angles and the side between the angles known.
The three common criterion to construct congruent triangles include:
 
Criteria
Description
Side-Side-Side congruence criterion (SSS)All three sides are given.
Side-Angle-Side congruence criterion (SAS)Any two sides and the angle between the sides are given.
Angle-Side-Angle congruence criterion (ASA)Any two angles and the sides between the angles given.
 
Let us look at each of the criterion in detail in the upcoming sections.