Olympiad Test: Symmetry - 1 - Class 6 MCQ

In standard block (capital) letters, H has two lines of symmetry:
a vertical axis through the middle (left and right vertical strokes mirror each other), and
a horizontal axis through the middle bar (top and bottom parts mirror). The others do not have two distinct mirror axes: A typically has only a vertical axis, B has a vertical axis but not a horizontal one that maps top loop to bottom loop, and C has at most one horizontal axis in some fonts — not two.

A square is a regular 4-gon, so it has 4 lines of reflection symmetry: two lines through the midpoints of opposite sides (vertical and horizontal) and two along the diagonals. Each of these axes maps the square exactly onto itself, so total = 4.

An equilateral triangle is unchanged by rotation through 120°, 240°, and 360° (the starting position). That gives 3 distinct positions in a full turn, so the rotational symmetry order = 3. (Order = 360° ÷ smallest nonzero rotation = 360° ÷ 120° = 3.)

Rotation by 180° maps the figure to itself twice during a full 360° turn: at 0° and at 180°. So there are 2 distinct orientations that coincide with the original — hence rotational symmetry of order 2. (Order = 360° ÷ 180° = 2.)

The digit 8 (in block/digital style) has two lines of symmetry: a vertical axis and a horizontal axis — both reflect the shape onto itself. The other digits listed do not have a full vertical or horizontal mirror that maps the digit exactly onto itself in typical block font.

A non-square rectangle has two lines of symmetry: the vertical line through the midpoints of the shorter sides and the horizontal line through the midpoints of the longer sides. The diagonals are not symmetry axes unless the rectangle is also a square, so total = 2.

A regular hexagon repeats under rotations of 60° increments: 60°, 120°, 180°, 240°, 300°, and 360°. That is 6 positions in one full rotation, so the order of rotational symmetry is 6 (360° ÷ 60° = 6).

A scalene triangle has all three sides of different lengths and all angles different, so there is no axis that maps the triangle onto itself — therefore no line of symmetry. By contrast, an isosceles triangle has 1 axis, a square has 4, and a circle has infinitely many.

Assuming a clock face with 12 identical, evenly spaced hour markers (i.e., an ideal regular 12-point design), the arrangement matches a regular 12-gon. A regular 12-gon has 12 axes of reflection: 6 axes pass through opposite hour marks (e.g., 12–6, 1–7) and 6 pass through midpoints between opposite marks — total 12. (Note: if the face shows different-looking numerals or decorations that are not symmetric, some or all reflection axes may be broken, but the regular evenly-marked clock has 12 reflection lines.)

Order of rotational symmetry = 360° ÷ (smallest rotation that maps the figure onto itself). Here 360° ÷ 45° = 8. So the figure has 8-fold rotational symmetry (it lines up 8 times during a full turn: 45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°).