ABC is congruent to GHE describe a sequence of transformations from ABC to GHE that proves their congruences
To prove the congruence between ABC and GHE, we can use the following sequence of transformations:
1. Translation: Move triangle GHE so that point G coincides with point A.
This transformation preserves distances and angles.
Now, the new triangle GHE overlaps with triangle ABC.
2. Rotation: Rotate the triangle GHE about point G
until side GH coincides with side AB.
This rotation preserves distances and angles.
Now, the new triangle GHE has side GH overlapping side AB.
3. Reflection: Reflect the triangle GHE across line GH.
This reflection preserves distances and angles.
Now, the new triangle GHE has side GH overlapping side AB and side HE overlapping side AC.
4. Translation: Move the triangle GHE so that point G coincides with point A again.
This transformation preserves distances and angles.
Now, the new triangle GHE is fully overlapping with triangle ABC.
After these transformations, triangle ABC and triangle GHE are now congruent, as all corresponding sides and angles are equal.