What is the sequence of transformations needed to move triangle ABC to triangle EGH to show that the triangles are congruent
In order to show that triangles ABC and EGH are congruent, we need to identify the sequence of transformations that would move triangle ABC onto triangle EGH. The following sequence of transformations will achieve this:
1. Translation: Move triangle ABC horizontally so that point A coincides with point E. The translation vector is defined by the difference in x-coordinate between A and E, and the same for the y-coordinate.
2. Rotation: Rotate triangle ABC about point A so that side AB coincides with side EG. The angle of rotation is the angle formed between AB and EG.
3. Reflection: Reflect triangle ABC across the line that contains side AB. This will result in side AC coinciding with side EH.
4. Translation: Finally, move the entire triangle ABC vertically so that point C coincides with point H. The translation vector is defined by the difference in x-coordinate between C and H, and the same for the y-coordinate.
After carrying out these transformations in sequence, triangle ABC will overlap with triangle EGH, proving that they are congruent.