Question

Which best explains whether or not all isosceles triangles are similar? All isosceles triangles are similar. Two angles within each triangle are always congruent. All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle. All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Answer 1

By Angle-Angle  simlilarity postulate :
If two angles of one triangle congruent to two angles of another, then triangles must be similar.
So, I think the answer is
All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Because two base angles in  isosceles triangle are congruent, but it could be a lot of isosceles triangles that have different  congruent base angles.
 For example,
45-45-90 is an isosceles triangle, and 30-30-120 is an isosceles triangles, but they do not have 2 congruent angles.