how can we prove that triangles are congruent?

How Can We Prove that Triangles Are Congruent?

Two triangles are congruent if and only if all their corresponding sides and angles are congruent.

http://library.thinkquest.org/20991/geo/ctri.html

In the example, triangle ABC and triangle XYZ are both congruent. You can tell becasue line AB and line XY have the same side measure of 10 units. Also, both triangles have the same angle measures in the same parts of the triangle. The sum of 65 and 75 is 140. To find the missing angle, you take the sum os the two existing measures and subtract it from 180. You'd get 40, and to check it  you'd add all the numbers to get 180.

The triangles are congruent because they both have the same measurments of all sides and angles.