Think about the order of the vertices in the statement.
Error: The order of the vertices in the triangle names is incorrect. Example Correction: △ TUV ≅ △ ZYX by the SSS Congruence Theorem
Practice makes perfect
Looking at the given triangles and the congruence statement, we can see that the correct theorem was used. Side-Side-Side makes sense to show congruence of the two triangles because we are shown three pairs of congruent segments. Now, let's consider the given names of the triangles.
△ TUV ? ≅ △ XYZ
The following diagram illustrates the order of the vertices as they have been named in the statement. You can follow the naming using the arrows or the color-scheme, blue- green- red.
The order of the vertices in the names are all incorrect! When naming congruent triangles, the congruent angles should be in the same order on both sides of the congruence statement. The following table includes all the possibilities of correct names.
Left-hand Triangle Name
≅
Right-hand Triangle Name
â–³ TUV
≅
â–³ ZYX
â–³ TVU
≅
â–³ ZXY
â–³ UTV
≅
â–³ YZX
â–³ UVT
≅
â–³ YXZ
â–³ VTU
≅
â–³ XZY
â–³ VUT
≅
â–³ XYZ
Therefore, a possible corrected statement could be:
△ TUV ≅ △ ZYX
by the SSS Congruence Theorem.
