Let's solve the problem of finding the
order of rotational symmetry for each shape in the image. The
order of rotational symmetry is the number of times a shape looks exactly the same as it rotates through 360°.
We'll go through each shape one by one:
---
a) Square (diamond orientation)
- This is a square, rotated so it looks like a diamond.
- A square has
4 lines of symmetry and
rotational symmetry of order 4.
- It looks the same after rotations of 90°, 180°, 270°, and 360°.
-
✔ Order of 4
---
b) Right triangle
- This is a right-angled triangle (not equilateral or isosceles).
- A scalene or right triangle (with no equal sides) has
no rotational symmetry except at 360°.
- So, it only looks the same once per full rotation.
-
✔ Order of 1
---
c) Regular Pentagon
- A regular pentagon has 5 equal sides and angles.
- It looks the same every 72° (360° ÷ 5 = 72°).
- Rotations: 72°, 144°, 216°, 288°, 360° → 5 times.
-
✔ Order of 5
---
d) Double arrow (horizontal arrows pointing left and right)
- This shape is symmetric horizontally but not vertically.
- If you rotate it 180°, it will look the same (the arrows swap places but still match).
- But at 90° or 270°, it doesn't look the same.
- So, it matches only at 0° and 180° → 2 positions.
-
✔ Order of 2
---
e) Parallelogram
- A general parallelogram (not a rhombus, rectangle, or square).
- It has rotational symmetry of
order 2 because:
- At 180° rotation, it maps onto itself.
- At 90°, 270°, etc., it does not.
-
✔ Order of 2
---
f) Regular Octagon (8-sided shape)
- This is a regular octagon (all sides and angles equal).
- It has rotational symmetry every 45° (360° ÷ 8 = 45°).
- So, it looks the same 8 times during a full rotation.
-
✔ Order of 8
---
✔ Final Answers:
a)
4
b)
1
c)
5
d)
2
e)
2
f)
8
---
🔍 Summary:
| Shape | Order of Rotational Symmetry |
|-------|-------------------------------|
| a) Square | 4 |
| b) Right Triangle | 1 |
| c) Pentagon | 5 |
| d) Double Arrow | 2 |
| e) Parallelogram | 2 |
| f) Octagon | 8 |
Let me know if you'd like a visual explanation or diagram!
Parent Tip: Review the logic above to help your child master the concept of printable shapes for rotational symmetry.
