△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to △GHE that proves their congruence.,
To prove that △ABC is congruent to △GHE, we need to perform a sequence of transformations that preserve shape and size.
1. Translation: We can start by translating △ABC so that point A coincides with point G. Since corresponding parts of congruent triangles are in the same position, this translation will ensure that △ABC and △GHE have one pair of corresponding sides (side AG and side GH) that are congruent.
2. Rotation: After translating △ABC, we can rotate it clockwise or counterclockwise until line AB is aligned with line GH. This rotation will preserve congruency of corresponding angles, resulting in △ABC and △GHE having two pairs of corresponding angles that are congruent (angle B and angle E, and angle C and angle H).
3. Reflection: Finally, we can reflect △ABC over the line bisecting angle A, so that point B coincides with point E and point C coincides with point H. This reflection will ensure that the remaining pair of corresponding sides, side BC and side HE, are congruent.
After performing these three transformations, we have shown that △ABC is congruent to △GHE.