Symmetrical Figures worksheet for students to identify and draw lines of symmetry for various geometric shapes.

Symmetrical Figures Problem Solution

The task is to identify and draw a line of symmetry for each shape provided. A line of symmetry is a line that divides a shape into two identical halves, such that one half is the mirror image of the other.

Let's analyze each shape step by step:

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#### 1. Hexagon
- Shape: A regular hexagon.
- Line of Symmetry: The dashed red line is already drawn vertically through the center.
- Explanation: A regular hexagon has 6 lines of symmetry, but the given line is one of them. It divides the hexagon into two identical halves, with each half being a mirror image of the other.

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#### 2. Trapezoid
- Shape: An irregular trapezoid.
- Line of Symmetry: Draw a vertical line down the middle.
- Explanation: The trapezoid appears symmetrical along its vertical axis. Drawing a vertical line through the midpoint of the top and bottom bases will divide it into two identical halves.

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#### 3. Star
- Shape: A five-pointed star.
- Line of Symmetry: Draw a vertical line down the middle.
- Explanation: A five-pointed star has multiple lines of symmetry (5 in total), but the simplest one to draw is the vertical line through the center. This line divides the star into two identical halves.

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#### 4. Rectangle
- Shape: A rectangle.
- Line of Symmetry: Draw a horizontal or vertical line through the center.
- Explanation: A rectangle has two lines of symmetry: one horizontal and one vertical. Either line will divide the rectangle into two identical halves. For simplicity, we can choose the vertical line.

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#### 5. Circle
- Shape: A circle.
- Line of Symmetry: Draw any straight line passing through the center.
- Explanation: A circle has infinite lines of symmetry because any line passing through its center will divide it into two identical halves. For this example, we can draw a horizontal or vertical line.

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#### 6. Sector of a Circle
- Shape: A sector of a circle (like a slice of pie).
- Line of Symmetry: Draw a line from the center of the circle to the midpoint of the arc.
- Explanation: The sector is symmetrical about the line that passes through its center and bisects the arc. This line divides the sector into two identical halves.

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#### 7. Arrow
- Shape: An arrow.
- Line of Symmetry: Draw a vertical line down the middle.
- Explanation: The arrow is symmetrical along its vertical axis. Drawing a vertical line through the center will divide it into two identical halves.

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#### 8. Diamond (Rhombus)
- Shape: A diamond (rhombus).
- Line of Symmetry: Draw either a vertical or diagonal line through the center.
- Explanation: A rhombus has two lines of symmetry: one vertical and one diagonal. For simplicity, we can choose the vertical line, which divides the rhombus into two identical halves.

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Final Answer:

Here are the lines of symmetry for each shape:

1. Hexagon: Vertical line (already drawn).
2. Trapezoid: Vertical line through the center.
3. Star: Vertical line through the center.
4. Rectangle: Vertical line through the center.
5. Circle: Horizontal or vertical line through the center.
6. Sector of a Circle: Line from the center to the midpoint of the arc.
7. Arrow: Vertical line through the center.
8. Diamond (Rhombus): Vertical line through the center.

Boxed Final Answer:
\[
\boxed{
\text{See explanations above for each shape.}
}
\]