triangle ABC is congruent to triangle GHE. describe a sequence of transformations from triangle ABC to triangle GHE that proves their congruence
To prove the congruence between triangle ABC and triangle GHE, we can use a sequence of transformations. Here is one possible sequence:
1. Translation: Start by performing a translation so that vertex A aligns with vertex G. This moves triangle ABC without changing its size or shape, and the result is triangle GBC.
2. Rotation: Rotate triangle GBC clockwise around point G until segment GB coincides with segment GH. Note that the angle of rotation should be such that vertex G remains stationary. After the rotation, the triangle becomes GHE.
3. Reflection: Reflect triangle GHE across the line GH. This reflection swaps the positions of the vertices, making vertex G coincide with vertex H.
After applying these three transformations (translation, rotation, and reflection) in the described order, triangle ABC will have transformed into triangle GHE. Since each transformation preserves size and shape, the triangles will be congruent.