Can two triangles not be congruent but five elements in triangle are same

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Can two triangles not be congruent but five elements in triangle are same


There are 3 sides and 3 angles in triangle. All 3 sides and 3 angles are collectively called 6 elements

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I'll assume that by "elements" OP means side lengths and angles.

Let triangle $ABC$ have sides $AB$ of length $8$, $BC$ of length $12$, and $AC$ of length $18$. Let triangle $XYZ$ have sides $XY$ of length $12$, $YZ$ of length $18$, and $XZ$ of length $27$.

Then the triangles are similar, since $|AB|/|XY|=|BC|/|YZ|=|AC|/|XZ|=2/3$. So $\angle A=\angle X$, $\angle B=\angle Y$, and $\angle C=\angle Z$.

Also, $|BC|=|XY|=12$, and $|AC|=|YZ|=18$. So, five elements are equal, but the triangles are manifestly not congruent.