https://file.aiquickdraw.com/mathbot/file/17285828379513wij6zns.jpg

Let's analyze the image and questions.

### First question: **Which rigid motion will verify that ∆ABC ≅ ∆A'B'C'?**

To identify the rigid motion between ∆ABC and ∆A'B'C', observe the following:
- The original triangle ∆ABC is reflected across the **y-axis** to obtain ∆A'B'C'. This can be seen by how point A, which is at (4, 1), becomes point A' at (-4, 1). Similarly, points B and C reflect across the y-axis.

Thus, the correct rigid motion is:
**C: Reflection over the y-axis**.

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### Second question: **Which statement is TRUE about the results of the transformation?**

Rigid motions (such as reflections) preserve both the **corresponding angles and corresponding side lengths** of geometric figures. Therefore, triangles ∆ABC and ∆A'B'C' are **congruent**, meaning both their corresponding sides and angles are equal.

Thus, the correct statement is:
**B: Only corresponding angles of the triangles are congruent after the transformation**.

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Would you like further details on this solution or have any questions?

Here are 5 related questions to deepen your understanding:
1. What properties are preserved under a reflection?
2. How can you verify that two triangles are congruent using transformations?
3. What is the difference between a reflection and a rotation?
4. How would a reflection over the x-axis change the positions of ∆ABC?
5. What other transformations (besides reflections) can maintain triangle congruence?

**Tip**: In geometry, rigid motions (translations, reflections, and rotations) always preserve the size and shape of figures, making them ideal for verifying congruence.

Which rigid motion will verify that ∆ABC ≅ ∆A'B'C'? Which statement is TRUE about the results of the transformation?

This problem involves identifying the correct rigid motion to verify that ∆ABC is congruent to ∆A'B'C'. Explore how a reflection over the y-axis preserves congruence by maintaining both corresponding angles and side lengths. Suitable for students in Grades 8-10.

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