a shape with a line of symmetry
The 2D shape which has one line of symmetry is the trapezium.
An isosceles triangle has one line of symmetry
A symmetrical shape. There are many different shapes that have one or more lines of symmetry and there is no other name associated with them as a group.
no
Not necessarily.
square
How about an isosceles triangle which has one line of symmetry
the shape is a heart.
An isosceles triangle and a kite have only one line of symmetry.
An isosceles triangle
Every right circular cone, conic section, and regular polygon has at least one line of symmetry.