Answer:
Yes, "All isosceles triangles with congruent vertex angles are similar".
Step-by-step explanation:
Consider the provided statement.
All isosceles triangles with congruent vertex angles are similar.
As we know that the two sides of an isosceles triangle are same.
It is given that the isosceles triangles with congruent vertex angles.
If vertex angles are congruent it means the opposite side of those angles are congruent. Also the sums of the base angles are the same,
As we know the base angles of an isosceles triangle are congruent, so by the AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
Or
let say ΔABC and ΔDEF are isosceles triangles where AB=DE and AC=DF
It means ∠B=∠E and ∠C=∠F also it is given that ∠A=∠D
Thus. from AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
