Problem Analysis:
The task involves identifying the
rotational symmetry of various geometric shapes. Rotational symmetry is defined as the property of a shape that allows it to look identical after being rotated by a certain angle around its center. The
order of rotational symmetry is the number of times the shape looks the same during a full rotation (360°).
Solution Explanation:
#### 1.
Square
-
Shape: A square has all sides equal and all angles equal to 90°.
-
Rotational Symmetry:
- When rotated by 90°, the square looks the same.
- It will look the same at 180°, 270°, and 360° rotations.
- Total: 4 positions where the square looks identical.
-
Order of Rotational Symmetry:
4
#### 2.
Rectangle
-
Shape: A rectangle has opposite sides equal and all angles equal to 90°.
-
Rotational Symmetry:
- When rotated by 180°, the rectangle looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the rectangle looks identical.
-
Order of Rotational Symmetry:
2
#### 3.
Rhombus
-
Shape: A rhombus has all sides equal but angles may differ.
-
Rotational Symmetry:
- When rotated by 180°, the rhombus looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the rhombus looks identical.
-
Order of Rotational Symmetry:
2
#### 4.
Kite
-
Shape: A kite has two pairs of adjacent sides equal.
-
Rotational Symmetry:
- The kite does not look the same after any rotation other than 360°.
- Total: 1 position where the kite looks identical.
-
Order of Rotational Symmetry:
1
#### 5.
Parallelogram
-
Shape: A parallelogram has opposite sides equal and parallel.
-
Rotational Symmetry:
- When rotated by 180°, the parallelogram looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the parallelogram looks identical.
-
Order of Rotational Symmetry:
2
#### 6.
Equilateral Triangle
-
Shape: An equilateral triangle has all sides equal and all angles equal to 60°.
-
Rotational Symmetry:
- When rotated by 120°, the triangle looks the same.
- It will also look the same at 240° and 360° rotations.
- Total: 3 positions where the triangle looks identical.
-
Order of Rotational Symmetry:
3
#### 7.
Isosceles Trapezium
-
Shape: An isosceles trapezium has one pair of parallel sides and the non-parallel sides are equal.
-
Rotational Symmetry:
- The isosceles trapezium does not look the same after any rotation other than 360°.
- Total: 1 position where the trapezium looks identical.
-
Order of Rotational Symmetry:
1
#### 8.
Hexagon
-
Shape: A regular hexagon has all sides equal and all angles equal.
-
Rotational Symmetry:
- When rotated by 60°, the hexagon looks the same.
- It will also look the same at 120°, 180°, 240°, 300°, and 360° rotations.
- Total: 6 positions where the hexagon looks identical.
-
Order of Rotational Symmetry:
6
Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{Square} & \text{Order 4} \\
\text{Rectangle} & \text{Order 2} \\
\text{Rhombus} & \text{Order 2} \\
\text{Kite} & \text{Order 1} \\
\text{Parallelogram} & \text{Order 2} \\
\text{Equilateral Triangle} & \text{Order 3} \\
\text{Isosceles Trapezium} & \text{Order 1} \\
\text{Hexagon} & \text{Order 6} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of rotational symmetry worksheet with answers.
