ABC is congruent to ghe describe a sequence of Transformations from ABC to ghe that proves their congerance

Answer 1

To prove that ABC is congruent to GHE, we need to perform a sequence of transformations that preserve shape and size.

1. Translation: Start by translating point A to point G in such a way that vector AG is equal to vector GH. This will move triangle ABC to GBC while preserving its shape and size.

2. Rotation: Rotate triangle GBC around point G by the necessary angle so that side BC is aligned with side HE, and vertex G coincides with vertex H. This rotation will bring GBC to GHC while maintaining their congruency.

3. Reflection: Finally, reflect triangle GHC over line GH to obtain triangle GHE. This reflection will swap the positions of vertices C and E while preserving their congruency with corresponding sides and angles.

By performing these transformations in sequence, we have successfully transformed ABC into GHE while proving their congruency.