Final answer:
Two isosceles triangles with congruent base angles are congruent sometimes.
Step-by-step explanation:
Two isosceles triangles with congruent base angles are congruent sometimes.
If two isosceles triangles have congruent base angles, it does not necessarily mean that they are congruent. Congruence of triangles depends on the congruency of corresponding sides and angles. In the case of isosceles triangles, if the corresponding sides and angles of two triangles are congruent, then the triangles are congruent.
For example, if triangle ABC and triangle DEF have congruent base angles, but the lengths of their corresponding sides are different, the triangles are not congruent. However, if their corresponding sides and angles are congruent, then the triangles are congruent.