My favorite theorem is the hypotenuse-leg theorem. It states that in the triangles ABC and DEF that if angle A and D are right angles and BC=EF and AB=DE. Then triangle ABC is congruent to triangle DEF. That is if a triangle and a hypotenuse and a leg matching then they are congruent.
I like this theorem because you do not need to know the inscribed angle between the two sides you just need to know that there is a right angle and the hypotenuse and a leg are equal in the 2 triangles.
