triangle ABC is congruent to triangle GHE Describe a sequence of transformations from triangle ABC to triangle GHE that proves their congruence.
To prove that triangle ABC is congruent to triangle GHE, we can use a sequence of transformations:
1. Translation: Move triangle ABC to a new position such that point A coincides with point G.
- This transformation preserves the shape and size of the triangle.
- Now, we'll refer to the new position as triangle A'B'C'.
2. Rotation: Rotate triangle A'B'C' clockwise or counterclockwise until side A'B' aligns with side GH.
- This rotation preserves the shape and size of the triangle.
- After the rotation, we'll refer to the new position as triangle A''B''C''.
3. Reflection: Reflect triangle A''B''C'' over a line that passes through side B''C'' and is perpendicular to it.
- This reflection preserves the shape and size of the triangle.
- After the reflection, we'll refer to the new position as triangle A'''B'''C'''.
Therefore, triangle ABC is congruent to triangle GHE due to the sequence of transformations.