Which statement about this figure is true?
It has reflectional symmetry with 22 lines of symmetry.
It has rotational symmetry with an angle of rotation of 45°.
It has no reflectional symmetry.
It has point symmetry.
No figure. Cannot copy and paste here.
To determine which statement about the figure is true, we need to understand the concepts of symmetry in geometry.
1. Reflectional Symmetry: If a figure can be divided into two equal halves by a line of reflection, it has reflectional symmetry. To find the number of lines of symmetry, we need to identify the lines that can divide the figure into two equal halves.
2. Rotational Symmetry: If a figure can be rotated by a certain angle around a point and still appear the same, it has rotational symmetry. The angle of rotation is the smallest angle by which the figure can be rotated to coincide with its original position.
3. Point Symmetry: If a figure can be rotated 180 degrees around a point and still appear the same, it has point symmetry. This is also known as rotational symmetry with an angle of rotation of 180°.
Now, let's evaluate each statement:
Statement 1: "It has reflectional symmetry with 22 lines of symmetry."
To assess this statement, visually examine the figure and determine if there are any lines that can divide it into two equal halves. Count them to verify if there are indeed 22 lines of symmetry.
Statement 2: "It has rotational symmetry with an angle of rotation of 45°."
Again, visually inspect the figure and check if it can be rotated by an angle of 45 degrees around a point and still look the same. If it does, the statement is true.
Statement 3: "It has no reflectional symmetry."
Once more, visually analyze the figure to see if any lines can divide it into two equal halves. If there are no such lines, the statement is true.
Statement 4: "It has point symmetry."
Check if the figure can be rotated 180 degrees around a point and still appear unchanged. If so, the statement is true.
By following these steps, you can examine the figure and evaluate which statement accurately describes its properties.