Question

Transformations and Congruence Unit Test
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Question
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.

Answer 1

To prove that △ABC is congruent to △GHE, a sequence of transformations can be used. Here is a possible sequence of transformations:

1. Translation: Translate △ABC 3 units to the left and 2 units up to get △A'B'C', with vertices marked at (-2, -1), (-2, 1), and (1, -1).

2. Reflection: Reflect △A'B'C' over the y-axis to get △A''B''C'', with vertices marked at (2, -1), (2, 1), and (-1, -1).

3. Rotation: Rotate △A''B''C'' 180 degrees counterclockwise about the origin to get △A'''B'''C''', with vertices marked at (-2, 1), (-2, -1), and (1, 1).

4. Translation: Translate △A'''B'''C''' 2 units to the right and 4 units down to get △GHE, with vertices marked at (-4, 2), (-4, -2), and (-1, 2).

By performing these transformations, we have proven that △ABC is congruent to △GHE.