Geometry 1.5 Line & Rotational Symmetry Draw 1. 2. 3. 4 ... - Free Printable

To solve the problems in the image, we will address each section step by step. Let's go through them one by one.

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Section 1: Draw the line(s) of symmetry for each shape. State how many lines you draw. If none, write 0.

#### Shape 1:
- The shape is a square.
- A square has 4 lines of symmetry: two diagonals and two lines passing through the midpoints of opposite sides.
- Answer: 4

#### Shape 2:
- The shape is a triangle (equilateral).
- An equilateral triangle has 3 lines of symmetry: one through each vertex and the midpoint of the opposite side.
- Answer: 3

#### Shape 3:
- The shape is a parallelogram that is not a rectangle or rhombus.
- A general parallelogram has 0 lines of symmetry.
- Answer: 0

#### Shape 4:
- The shape is a circle.
- A circle has infinite lines of symmetry, but typically we say it has any diameter as a line of symmetry.
- Answer: Infinite (or "many")

#### Shape 5:
- The shape is a regular pentagon.
- A regular pentagon has 5 lines of symmetry: one through each vertex and the midpoint of the opposite side.
- Answer: 5

#### Shape 6:
- The shape is a spiral.
- A spiral generally has 0 lines of symmetry because it does not have any reflective symmetry.
- Answer: 0

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Section 2: Tell whether the dotted line on each shape represents a line of symmetry. Write yes or no.

#### Shape 7:
- The shape is a rectangle with a dotted line passing through the midpoints of two opposite sides.
- This is a line of symmetry for a rectangle.
- Answer: Yes

#### Shape 8:
- The shape is a snowflake with a dotted line passing through two opposite points.
- This is a line of symmetry for the snowflake.
- Answer: Yes

#### Shape 9:
- The shape is a cross with a dotted line passing through the center horizontally.
- This is a line of symmetry for the cross.
- Answer: Yes

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Section 3: Determine the rotational order and angle of rotation for the following figures.

#### Figure 10: Star
- The star has 5 arms.
- Rotational Order: 5 (it looks the same after rotating by \( \frac{360^\circ}{5} = 72^\circ \)).
- Angle of Rotation: \( 72^\circ \)

#### Figure 11: Recycle Symbol
- The recycle symbol has 3 arrows.
- Rotational Order: 3 (it looks the same after rotating by \( \frac{360^\circ}{3} = 120^\circ \)).
- Angle of Rotation: \( 120^\circ \)

#### Figure 12: Parallelogram
- A general parallelogram has rotational symmetry of order 2 (180° rotation).
- Rotational Order: 2
- Angle of Rotation: \( 180^\circ \)

#### Figure 13: Arrow
- The arrow has no rotational symmetry other than a full 360° rotation.
- Rotational Order: 1
- Angle of Rotation: \( 360^\circ \)

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Section 4: Determine the following symmetry characteristics for these figures.

#### Figure 14: Triangle (Equilateral)
- Lines of Symmetry: 3 (through each vertex and the midpoint of the opposite side)
- Rotational Order: 3 (rotates to look the same at \( 120^\circ \) intervals)
- Angle of Rotation: \( 120^\circ \)

#### Figure 15: Letter Z
- Lines of Symmetry: 0 (no reflective symmetry)
- Rotational Order: 2 (rotates to look the same at \( 180^\circ \))
- Angle of Rotation: \( 180^\circ \)

#### Figure 16: Flower
- Lines of Symmetry: 5 (assuming it is a regular 5-petaled flower)
- Rotational Order: 5 (rotates to look the same at \( 72^\circ \) intervals)
- Angle of Rotation: \( 72^\circ \)

#### Figure 17: Square
- Lines of Symmetry: 4 (two diagonals and two lines through midpoints of opposite sides)
- Rotational Order: 4 (rotates to look the same at \( 90^\circ \) intervals)
- Angle of Rotation: \( 90^\circ \)

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Final Answers:

1. Square: 4
2. Triangle: 3
3. Parallelogram: 0
4. Circle: Infinite
5. Pentagon: 5
6. Spiral: 0
7. Rectangle: Yes
8. Snowflake: Yes
9. Cross: Yes
10. Star: Order 5, Angle \( 72^\circ \)
11. Recycle: Order 3, Angle \( 120^\circ \)
12. Parallelogram: Order 2, Angle \( 180^\circ \)
13. Arrow: Order 1, Angle \( 360^\circ \)
14. Triangle: Lines 3, Order 3, Angle \( 120^\circ \)
15. Letter Z: Lines 0, Order 2, Angle \( 180^\circ \)
16. Flower: Lines 5, Order 5, Angle \( 72^\circ \)
17. Square: Lines 4, Order 4, Angle \( 90^\circ \)

\boxed{4, 3, 0, \text{Infinite}, 5, 0, \text{Yes}, \text{Yes}, \text{Yes}, 5/72^\circ, 3/120^\circ, 2/180^\circ, 1/360^\circ, 3/3/120^\circ, 0/2/180^\circ, 5/5/72^\circ, 4/4/90^\circ}