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.
(2 points)
Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
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To prove that △ABC is congruent to △GHE, we can use a sequence of transformations.
1. Translation: We can translate triangle ABC 3 units to the left and 4 units up to coincide with triangle GHE. This would be a translation of vector <-3, 4>.
2. Reflection: After the translation, we can reflect triangle ABC over the y-axis to align it perfectly with triangle GHE.
3. Rotation: Finally, we can rotate triangle ABC 180 degrees counter-clockwise around the origin to coincide exactly with triangle GHE.
By performing these transformations, we can prove that △ABC is congruent to △GHE.