Final answer:
The error in the statement involves incorrectly listing the vertices in the congruence statement. The correct format should reflect corresponding sides for the SSS Congruence Theorem. The terms in each triangle must be in the order that pairs corresponding sides correctly.
Step-by-step explanation:
The statement "TUV = XYZ by the SSS Congruence Theorem" is in error because when using the SSS Congruence Theorem, we must specify that the corresponding sides of the two triangles are congruent. To write a correct congruence statement, we need to ensure that the order of vertices reflects the corresponding congruent sides. For example, if TU corresponds to XY, UV to YZ, and TV to XZ, then the correct statement would be ∆TUV ≅ ∆XYZ.
When dealing with congruent triangles, it's crucial not just to state that the triangles are congruent, but to match each vertex of one triangle with its corresponding vertex in the other triangle in the right order. This way, one can clearly see the one-to-one correspondence between the sides and the angles of the triangles.
Let's remember that the Pythagorean Theorem describes the relationship between the sides of a right-angled triangle and plays a role in finding the length of sides when testing for SSS congruence in right triangles, ensuring the triangles are indeed congruent when the sides squared and summed up equal the square of the longest side (hypotenuse).