## Elementary Geometry for College Students (5th Edition)

For any two isosceles triangles to be similar, the vertex angles of the two triangles need to be congruent. For example: I could have one isosceles triangle with angle measures of $80^{\circ}, 50^{\circ}, 50^{\circ}$, and one isosceles triangle with angle measures of $90^{\circ}, 45^{\circ}, 45^{\circ}$. These two isosceles triangles are NOT similar.