To prove that triangle ABC is congruent to triangle GHE, we can use the sequence of transformations:
1. Translation: Move triangle ABC two units to the right and three units up. This will result in a new triangle with vertices A(3, 0), B(3, 2), and C(6, 0).
2. Reflection: Reflect the translated triangle over the x-axis. This will result in a new triangle with vertices A(3, 0), B(3, -2), and C(6, 0).
3. Rotation: Rotate the reflected triangle 180 degrees counterclockwise about the origin. This will result in a new triangle with vertices E(-3, 0), G(-3, 2), and H(-6, 0).
The transformed triangle EGH, obtained after the translation, reflection, and rotation, is congruent to triangle ABC. Therefore, triangles ABC and GHE are congruent.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Two triangles, upper A upper B upper C and upper E upper G upper H, are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 1 comma negative 3 right parenthesis, upper B left parenthesis 1 comma negative 1 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 2 right parenthesis, and upper H left parenthesis negative 4 comma 2 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.
△ABC is congruent to △GHE . Describe a sequence of transformations from △ABC to △GHE that proves their congruence.
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