Problem: In the figure below, triangle ABC and triangle DEF are overlapping. Prove that triangle ABC is congruent to triangle DEF.

Image:

A / \ / \ / \ / \ / \ B-----------C \ / \ / \ / \ / \ / D \ \ \ \ \ E \ \ \ \ \ F

Solution:

To prove that triangle ABC is congruent to triangle DEF, we need to show that all corresponding sides and angles are congruent.

1. Side AB is congruent to side DE. (Given)
2. Side BC is congruent to side EF. (Given)
3. Side AC is congruent to side DF. (Given)
4. Angle A is congruent to angle D. (Given)
5. Angle B is congruent to angle E. (Given)
6. Angle C is congruent to angle F. (Given)

Since all corresponding sides and angles are congruent, triangle ABC is congruent to triangle DEF by the Side-Angle-Side (SAS) congruence criterion.