What are not congruence theorems?

Answer:
I am guessing you are interested in triangles. Here are two false triangle congruence theorem conjectures.
1, If the angles of one triangle are equal respectively to the angles of another triangle, the triangles are congruent. ( abbreviated AAA).

2. If two sides and one angle of a triangle are equal respectively the two sides and one angle of another triangle, the triangles are congruent. (abbreviated SSA)
Comment: Draw triangles with pairs of equal sides but in which the included angle between the equal sides is acute in one case and obtuse in the others.
Contributor: Jphelm
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