To determine the sequence of transformations needed to show that triangle ABC is congruent to triangle EGH, we need to align the two triangles precisely. Generally speaking, congruent triangles can be mapped onto each other using a combination of translations, rotations, and reflections.
Here’s how we can approach this:
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Translation: Move triangle ABC to a position where one of its vertices matches a corresponding vertex in triangle EGH. For instance, if point A in triangle ABC corresponds to point E in triangle EGH, translate triangle ABC so that A overlaps with E.
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Rotation: After translating, you might need to rotate triangle ABC around the point that you have aligned. This rotation should align the corresponding vertices of both triangles. For example, if after translation points A and E match, and you find that B aligns to G only after rotating around point E, you would perform the rotation at this point.
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Reflection (if necessary): If the triangles still do not match up perfectly after translation and rotation, you might need to perform a reflection over a line (which could be the line joining vertices E and G, or any relevant line of symmetry). This step aligns the remaining vertices of triangle ABC with triangle EGH.
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Verification: After performing these transformations, you should verify that each corresponding vertex of the triangles matches and that the triangles have the same size and shape.
In conclusion, the sequence of transformations typically involves translating triangle ABC to align with triangle EGH, followed by rotating it as needed, and possibly reflecting it to ensure all corresponding vertices align correctly. Note that the exact transformations may vary depending on the specific positions and orientations of the triangles.
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