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GATE 2025 AR — Planning – Question 9

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

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

  1. Circle; Square; Equilateral triangle; Isosceles triangle
  2. Isosceles triangle; Equilateral triangle; Square; Circle
  3. Equilateral triangle; Isosceles triangle; Square; Circle
  4. Isosceles triangle; Square; Equilateral triangle; Circle

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Show answer and explanation

Correct answer: (B) Isosceles triangle; Equilateral triangle; Square; Circle

Explanation

The intended isosceles triangle is non-equilateral and has one mirror line, through its apex and the midpoint of its base. An equilateral triangle has three, one through each vertex and opposite midpoint.

A square has four: two diagonals and the two lines through opposite side midpoints. A circle has infinitely many, since every diameter is a mirror line.

The increasing order is therefore **isosceles triangle, equilateral triangle, square, circle — B**. The non-equilateral convention matters because an equilateral triangle is also isosceles under the inclusive mathematical definition.

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