Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

The correct option is: Isosceles triangle; Equilateral triangle; Square; Circle

To find the correct sequence, we need to determine the number of mirror lines (lines of symmetry) for each shape and arrange them in increasing order.

A line of symmetry is a line that divides a shape into two identical halves, such that if you fold the shape along the line, both halves match exactly.

Let us analyze the number of lines of symmetry for each object:
1. Isosceles triangle: An isosceles triangle has two equal sides and one line of symmetry, which passes through the vertex between the equal sides to the midpoint of the base.
2. Equilateral triangle: An equilateral triangle has three equal sides and three lines of symmetry, one passing through each vertex to the midpoint of the opposite side.
3. Square: A square has four equal sides and four lines of symmetry: two passing vertically and horizontally through the midpoints of opposite sides, and two along its diagonals.
4. Circle: A circle has infinite lines of symmetry, as any line passing through the center of the circle divides it into two symmetrical halves.

Now, let's write down the number of mirror lines for each shape:

$$\text{Isosceles triangle (1)}<\text{Equilateral triangle (3)}<\text{Square (4)}<\text{Circle (infinite)}$$

Therefore, the sequence of objects arranged in the increasing number of mirror lines is: Isosceles triangle; Equilateral triangle; Square; Circle.