The postulate ASA (angle-side-angle) states that if two triangles have two congruent angles and one congruent side, then they are congruent triangles. The picture itself shows that angle ABC is congruent to angle CDE and that BC is equal to CD. Already you have that these two triangles one pair of congruent angles and congruent sides.
Looking at the picture, you can see that angles ACB and DCE are congruent. How? They form vertical angles, which are, by definition, equal to one another.
Therefore, you have two pairs of angles and a side congruent so ASA is the postulate used to prove congruency in this example
