If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.
Idea: A line of symmetry folds the shape into two matching halves.
Recall:
Let the triangle be ΔABC and suppose it is isosceles with two equal sides.
\(AB = AC\)
In any isosceles triangle, there is one obvious line of symmetry: the line through the vertex between the equal sides and the midpoint of the opposite side.
Now the question says there is more than one line of symmetry. So there must be a second line of symmetry as well.
If a second symmetry line goes through vertex B, it must also split the opposite side and make the two sides touching B equal:
\(AB = BC\)
We already had:
\(AB = AC\)
Combining both equalities gives:
\(AB = AC = BC\)
So all three sides are equal. That means the triangle is equilateral.
Conclusion: If an isosceles triangle has more than one line of symmetry, it cannot stay merely isosceles—it becomes equilateral. Therefore, the statement is true.