Does it Look the Same? - Quarter and Half Turns

Rotational Symmetry occurs when a shape looks exactly the same as its original position after being rotated by a certain angle around its center. If you can't tell that the shape has been moved, it has rotational symmetry.

A Half Turn ($\\frac{1}{2}$ turn) is a rotation of $180^\circ$, which is equivalent to turning an object upside down. For example, if you rotate the letter 'H' or 'S' by $180^\circ$, they look exactly the same as their original form.

A Quarter Turn ($\\frac{1}{4}$ turn) is a rotation of $90^\circ$. This is like the movement of a clock hand from $12$ to $3$. A square looks the same after a quarter turn, but a horizontal rectangle will look like a vertical rectangle after the same turn.

The Center of Rotation is the fixed point around which a shape turns. Imagine a pin stuck in the middle of a paper windmill; the pin is the center, and the blades rotate around it. The shape of the blades looks the same after specific turns depending on the number of blades.

One-Third ($\\frac{1}{3}$) and One-Sixth ($\\frac{1}{6}$) Turns: A $\\frac{1}{3}$ turn corresponds to $120^\circ$ and is commonly seen in equilateral triangles. A $\\frac{1}{6}$ turn corresponds to $60^\circ$ and is common in regular hexagons, which look identical after every $60^\circ$ rotation.

Symmetry in Digits and Letters: Some numbers and letters look the same after a half turn. The digits $0, 1,$ and $8$ look identical when turned upside down, while the letters $O, I, X, H, S, N,$ and $Z$ also retain their appearance after a $180^\circ$ rotation.

Visualizing Changes: To check if a shape looks the same after a turn, imagine the shape inside a circle. A $\\frac{1}{4}$ turn moves a point on the top to the right side, while a $\\frac{1}{2}$ turn moves a point from the top to the very bottom.