Choose the correct answer
Choose the correct answer
We need to imagine that we have two isosceles triangles with equal vertex angles.
If the vertex angle is equal, we can know that the other two angles are also equal, since in a triangle the sum of angles equals 180, and in an isosceles triangle the base angles are equal to each other, so the ratios are maintained between the triangles.
However, the first statement is incorrect, because this is triangle similarity, not congruence. Triangle congruence requires at least one equal side.
The second statement is also incorrect, because we don't know which of their angles are equal, it's possible that a base angle of one triangle is identical to the vertex angle of the second triangle, therefore they are not equal.
The third statement is correct, according to the logic we defined at the beginning.
The fourth statement is incorrect, because not all isosceles triangles are similar.
Therefore, we understand that answer C is correct.
Equal isosceles triangles
The main angle is similar