To determine which statement best describes the resulting triangles, let's analyze the given information in detail:
1. Given Data: We have a rectangle with a diagonal drawn from one corner to the opposite corner. This diagonal divides each of the rectangle's right angles (90°) into two smaller angles of 32° and 58°.
2. Triangles Formed: Drawing the diagonal in the rectangle forms two right triangles. Each of these right triangles has the same set of angles: 32°, 58°, and 90° (since the sum of the angles in any triangle is always 180°, and the triangles are right triangles with a 90° angle by definition).
3. Angle Analysis:
- Each triangle has angles of 32°, 58°, and 90°.
- Since both triangles have identical angle measures, they are similar by Angle-Angle (AA) similarity.
4. Congruence:
- In right triangles, if the angles are the same, the triangles are not just similar but also congruent (having the same shape and size) because the lengths of the corresponding sides will also be proportional and hence equal.
5. Conclusion: The two triangles not only share the same angles but are also congruent. However, they are oriented differently within the rectangle. One triangle is a mirror image of the other across the diagonal.
Therefore, the statement that best describes the resulting triangles is:
The two triangles are congruent but are oriented differently.
