To solve the problem of finding the
order of rotation for each shape, we need to determine how many times a shape can be rotated (in multiples of 360°/n) before it looks exactly the same as its original orientation. The order of rotation is the number of distinct orientations in which the shape appears identical during a full 360° rotation.
Step-by-Step Analysis of Each Shape:
#### 1.
Vertical Line (Rectangle)
- A vertical line has no rotational symmetry other than a full 360° rotation.
- It does not look the same at any other angle (e.g., 90°, 180°, or 270°).
-
Order of Rotation: 1
#### 2.
Star Shape
- The star shape has 5 points and rotational symmetry.
- It looks the same after rotating by \( \frac{360^\circ}{5} = 72^\circ \).
- There are 5 distinct orientations (0°, 72°, 144°, 216°, 288°).
-
Order of Rotation: 5
#### 3.
L-Shaped Figure
- The L-shaped figure does not have rotational symmetry.
- It does not look the same at any angle other than 360°.
-
Order of Rotation: 1
#### 4.
Circle
- A circle has infinite rotational symmetry because it looks the same at any angle.
- However, in the context of this problem, we typically consider the smallest non-trivial rotation that makes the shape look the same, which is 360°.
-
Order of Rotation: ∞ (or technically, any integer, but often considered as 1 for simplicity in such problems)
#### 5.
Z-Shaped Figure
- The Z-shaped figure does not have rotational symmetry.
- It does not look the same at any angle other than 360°.
-
Order of Rotation: 1
#### 6.
Four-Triangle Shape
- This shape has 4 triangles arranged symmetrically around a central point.
- It looks the same after rotating by \( \frac{360^\circ}{4} = 90^\circ \).
- There are 4 distinct orientations (0°, 90°, 180°, 270°).
-
Order of Rotation: 4
#### 7.
T-Shaped Figure with Crossbars
- The T-shaped figure with crossbars does not have rotational symmetry.
- It does not look the same at any angle other than 360°.
-
Order of Rotation: 1
Final Answer:
\[
\boxed{1, 5, 1, \infty, 1, 4, 1}
\]
If the circle is considered to have an order of 1 for simplicity, the answer would be:
\[
\boxed{1, 5, 1, 1, 1, 4, 1}
\]
Parent Tip: Review the logic above to help your child master the concept of printable shapes for rotational symmetry.
