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.

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.

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.