Olympiad Test: Symmetry - 2 - Class 6 MCQ

A circle can be folded along any diameter.
There are infinitely many diameters → infinite axes.

T → only 1 vertical axis.
M → 1 vertical axis too, but depends on font.
O → infinite axes.
N → no symmetry.
Safest choice = T.

Smallest rotation = 360° ÷ 8 = 45°.
So it matches at 8 positions → order = 8.

Scalene → 0 axes.
Isosceles → 1 axis (from vertex to base midpoint).
Square → 4 axes.
Circle → infinite axes.

Letter X has 4 axes of symmetry:
Vertical,
Horizontal,
Two diagonals.

A regular n-gon has n symmetry axes.
So a regular pentagon (n=5) has 5 axes.

An equilateral triangle has 3 equal sides and 3 equal angles.
Each axis of symmetry passes through a vertex and the midpoint of the opposite side.
Hence, it has 3 lines of symmetry.

Smallest rotation = 360° ÷ order = 360° ÷ 12 = 30°.

The letter H has:
Vertical axis (left ↔ right).
Horizontal axis (top ↔ bottom).
Other letters lack one of these.

A regular n-gon has n reflection axes.
So a regular decagon (n=10) has 10 lines of symmetry.