https://file.aiquickdraw.com/mathbot/file/17267559260494mpce6gb.jpg

Let's analyze the problem from the image. Here's a breakdown:

1. **Transformations Applied to Triangle ABC**:
   - The triangle is **reflected** across the y-axis.
   - Then it is **rotated** 30° about the origin.
   - Finally, it is **translated** 7 units to the left.
   - After these transformations, triangle A'B'C' is formed.

2. **Perimeter**:
   - Geometric transformations such as reflection, rotation, and translation **do not change the size or perimeter** of a shape. These transformations are rigid motions, meaning they preserve distances and angles.
   - Therefore, the perimeter of triangle A'B'C' will be **equal to** the perimeter of triangle ABC.

3. **Angle Measure**:
   - The second part of the problem asks which angle in triangle A'B'C' corresponds to the angle CAB in triangle ABC.
   - Since rotation and reflection do not change the angle measures but may change the order of the points, we need to determine which new angle corresponds to CAB based on the transformations.
     - After reflection and rotation, the angle at vertex A will change to another location, but the angle itself remains the same.
     - Based on typical order changes due to reflection and rotation, the angle CAB in triangle ABC will now be at angle **C'A'B'** in triangle A'B'C'.

### Conclusion:
- **CHOICE 1**: The perimeter of triangle A'B'C' will be **equal to** the perimeter of triangle ABC.
- **CHOICE 2**: The measure of angle CAB will now be equal to the measure of angle **C'A'B'**.

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Would you like a detailed explanation of any specific part? Here are 5 related questions to expand on this concept:

1. What are rigid transformations in geometry?
2. How does rotation affect the coordinates of a point?
3. Can reflection change the orientation of a triangle?
4. Why do translations not affect the perimeter of a shape?
5. What are the properties of congruent triangles?

**Tip**: When solving transformation problems, always check if the transformations are rigid motions, as they preserve size and shape!

Triangle ABC is reflected across the y-axis, rotated 30° about the origin, and translated 7 units to the left, resulting in triangle A'B'C'. The perimeter of triangle A'B'C' will be [CHOICE 1] the perimeter of triangle ABC. The measure of angle CAB will now be equal to the measure of angle [CHOICE 2].

Explore how triangle ABC undergoes a series of rigid transformations: reflection across the y-axis, rotation by 30°, and translation. Understand how these transformations affect the perimeter and angle measures, including how the angle CAB corresponds to a new angle in triangle A'B'C'.

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