https://file.aiquickdraw.com/mathbot/file/1728435560808aaxkjezt.jpg

Let's go over the problems from the image and work through their solutions step by step.

### Problem 14:
- **Part (a)** asks to name the rotation. The figure shows a parallelogram \( ABCD \) and its rotated form. Since this is a geometry problem, I would assume the rotation is around some axis or point, possibly 90° or 180°. However, the exact details are not visible from this part of the image.
- **Part (b)** asks to label the vertices \( A', B', C' \) of the rotated figure. This involves identifying how each vertex is mapped after the rotation.
- **Part (c)** involves finding \( \angle L'A'D'C' \), given \( \angle LADC = 30^\circ \). To solve this, you would typically use properties of rotational transformations or symmetry, but we'd need more specific coordinates or measures for precision.

### Problem 15:
This problem is about identifying examples of figures that satisfy certain symmetry properties:
- **(a)** Rotational symmetry with an angle of 90°
- **(b)** Rotational symmetry with angles of rotational symmetry of 72°
- **(c)** Rotational symmetry with an angle of 180°, two lines of reflectional symmetry
- **(d)** Rotational symmetry with an angle of 180°, no lines of reflectional symmetry

You would need to think of common geometric shapes, like squares, pentagons, etc., and their symmetry properties.

### Lesson 9-4 Practice Problems:
Let's break these down:

- **Problem 16** asks you to describe rotations that would move the arrow to different positions. Each subpart (a), (b), and (c) gives different final coordinates, and you need to describe the rotation that maps the initial arrow to those points.
  
- **Problem 17** asks you to identify the direction of the arrow after the given rotations (90° counterclockwise, 180°, and 90° clockwise) and specify the new positions.

- **Problem 18** involves describing a figure with rotational symmetry of 10°, which is less common but typically relates to figures like stars or highly regular polygons.

- **Problem 19** is a conceptual argument. You need to determine whether a figure can have a rotational symmetry of 37°, which is a non-standard angle for typical geometric figures, and explain why or why not.

Would you like to dive into the details of solving any of these problems? Let me know if you'd like more step-by-step explanations.

### 5 Related Questions:
1. How do you determine the rotation angle in a figure based on symmetry properties?
2. What are examples of figures with rotational symmetry of 90°, 72°, and 180°?
3. How can you apply transformation matrices to solve rotation problems in geometry?
4. How do reflectional symmetry and rotational symmetry differ in geometric figures?
5. Why are specific angles (like 37°) uncommon for rotational symmetry in regular polygons?

### Tip:
When working with rotational symmetry, remember that regular polygons often have symmetry angles related to 360° divided by the number of sides!

The figure shows a parallelogram ABCD and its rotation. Identify the rotation, label the rotated vertices, and solve for angle properties. Other questions involve identifying rotational symmetry for various figures and describing rotational movements.

Solve geometry problems involving the rotation of a parallelogram and identify rotational symmetry in different figures. Learn about rotational transformations, angle properties, and symmetry with detailed examples. Suitable for students in Grades 9-10.

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