△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, we need to perform a sequence of transformations that preserve shape, size, and orientation. Here's a possible sequence of transformations:
1. Translation: Translate △ABC so that point A coincides with point T. Since corresponding parts must coincide after transformation, it is important to maintain the order of the triangle vertices. We now have △ABC coinciding with △THE, with A coinciding with T.
2. Rotation: Rotate △ABC clockwise or counterclockwise around the point A (now coinciding with T) so that side AB coincides with side TH. Since we've already established the congruence of these triangles, the rotation will ensure the congruence of the remaining sides as well. Now, △ABC is transformed into △THE, with both triangles having sides AB and TH coinciding.
3. Reflection: Reflect △ABC over the line that contains the side AB (now coinciding with TH) to make side BC coincide with side HE. This reflection preserves shape, size, and orientation and ensures that side BC coincides with side HE. Now, △ABC is transformed into △THE, with sides AB, BC, and TH, HE coinciding.
After the sequence of transformations (translation, rotation, and reflection), △ABC is congruent to △THE.