Question

The sum of the lengths of the sides of one triangle equals the sum of the lengths of the sides of a second triangle. Are the two triangles congruent?

Answer 1

Of course not.
One triangle could have sides 3, 3, and 3, perimeter is 9
another could have sides 2, 3, 4 , perimeter is 9, but
clearly the angles are not the same as the angles of the first one.

Answer 2

Thanks for your opinion it really helps