Question
△ABC is congruent to △GHE . Describe a sequence of transformations from △ABC to △GHE that proves their congruence. Try a 90 CW rotation and then a translation. DONT USE SPECIAL CHARACTERS
Answers
GPT-4o mini
To show that triangle ABC is congruent to triangle GHE, we can use a sequence of transformations. Here’s how we can achieve this:
1. **Rotate Triangle ABC 90 degrees clockwise.**
- This transformation will change the orientation of triangle ABC. For example, if point A (x1, y1), B (x2, y2), and C (x3, y3) are the vertices of the triangle, after a 90-degree clockwise rotation, the new coordinates will be:
- A' (y1, -x1)
- B' (y2, -x2)
- C' (y3, -x3)
2. **Translate the rotated triangle to match triangle GHE.**
- After the rotation, adjust the position of triangle A'B'C' by translating it so that one of its vertices (let's say A') lands on the corresponding vertex of triangle GHE (let's say G).
- To do this, you can determine the required translation vector by finding the difference between the coordinates of G and A'.
After completing these steps, triangle ABC will be transformed into triangle GHE, proving their congruence through rotation and translation.
1. **Rotate Triangle ABC 90 degrees clockwise.**
- This transformation will change the orientation of triangle ABC. For example, if point A (x1, y1), B (x2, y2), and C (x3, y3) are the vertices of the triangle, after a 90-degree clockwise rotation, the new coordinates will be:
- A' (y1, -x1)
- B' (y2, -x2)
- C' (y3, -x3)
2. **Translate the rotated triangle to match triangle GHE.**
- After the rotation, adjust the position of triangle A'B'C' by translating it so that one of its vertices (let's say A') lands on the corresponding vertex of triangle GHE (let's say G).
- To do this, you can determine the required translation vector by finding the difference between the coordinates of G and A'.
After completing these steps, triangle ABC will be transformed into triangle GHE, proving their congruence through rotation and translation.