ABC is congruent to △GHI . Describe a sequence of transformations from △ABC to △THE that proves their congruence.
To prove that △ABC is congruent to △THE, a sequence of transformations can be applied: a translation to align the initial vertex A with point G, a rotation around point A to make GH coincide with BC, a translation to align H with B, and a final translation to align I with C.
To prove that △ABC is congruent to △THE, we need to describe a sequence of transformations that will show that they are congruent. Here is one possible sequence of transformations:
1. Translation: Move △GHI so that point G coincides with point A. This will establish △ABC and △GHI share the same initial vertex A.
2. Rotation: Rotate △GHI around point A, so that segment GH coincides with segment BC. This will make the sides GH and BC parallel and congruent.
3. Translation: Move △GHI so that point H coincides with point B. This will align △GHI with △ABC, with points G and H coinciding with points A and B respectively.
4. Translation: Move △GHI so that point I coincides with point C. This final translation will ensure that all three corresponding points G, H, and I coincide with the corresponding points in △ABC (A, B, C).
By performing these four transformations, it is demonstrated that △ABC and △GHI are congruent to △THE.