Question

△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to △GHE that proves their congruence. dont make it so confusing step by step and easy to understand

Answer 1

We want a rigid-motion sequence that carries A→G, B→H, C→E. Do this in simple steps:

1. Translate triangle ABC so point A lands on G. (Shift every point by the vector from A to G.)

2. Rotate the translated triangle about G until the image of B lies on H. (Turn around G by the angle needed to make the segment that was AB coincide with GH.)

3. Check the image of C:
- If that image is exactly E, you are done (the translation + rotation carried C to E).
- If the image of C is on the opposite side of GH from E, reflect the triangle across the line GH. That reflection takes the image of C to E.

Either way, after these moves A maps to G, B maps to H, and C maps to E, so △ABC is congruent to △GHE (rigid motions preserve distances).