Geometry: Symmetrical Figures CCSS 4.G.3 Worksheets & Activities ... - Free Printable

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 vertical, dividing the hexagon into two identical halves.

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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, as the left and right sides are mirror images of each other.

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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 to draw is the vertical line through the center, which divides the star into two identical halves.

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#### 4. Rectangle
- Shape: A rectangle.
- Line of Symmetry: Draw a horizontal line through the center.
- Explanation: A rectangle has two lines of symmetry: one horizontal and one vertical. Here, we choose the horizontal line because it divides the rectangle into two identical halves.

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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, as any line passing through its center will divide it into two identical halves. For simplicity, draw a vertical or horizontal 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 along the line that passes through its center and bisects the arc.

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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, as the left and right sides are mirror images of each other.

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#### 8. Diamond (Rhombus)
- Shape: A diamond (rhombus).
- Line of Symmetry: Draw a diagonal line from one corner to the opposite corner.
- Explanation: A rhombus has two lines of symmetry: the two diagonals. Drawing either diagonal will divide the rhombus into two identical halves. Here, we choose one diagonal.

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Final Answer:

For each shape, the lines of symmetry are as follows:

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

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