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None; because there is no justification for assuming that the two triangles (or trangles, as you prefer to call them) are similar.
Yes, triangles ABC and DEF are congruent if all corresponding sides and angles are equal. The congruence postulate that applies in this case could be the Side-Angle-Side (SAS) postulate, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Other applicable postulates include Side-Side-Side (SSS) and Angle-Angle-Side (AAS), depending on the known measurements.
Pythagorus did hints the name "Pythagoream Theorem."
The Pythagorean theorem gets its name from the ancient Greek mathematician Pythagoras. He was one of the first to offer proof of the theorem.
The theorem emulates the action of a hinge. As the angle of the hinge is increased the distance between the free edges increases.