Transformations and Congruence Unit Test

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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)

Answer 1

The sequence of transformations from triangle ABC to triangle GHE that proves their congruence is as follows:

1. Translation: Move triangle ABC 3 units to the left and 8 units up to align point A with point E. This will translate the entire triangle ABC to align with triangle GHE.

2. Rotation: Rotate the translated triangle ABC 180 degrees clockwise around point E (the origin) to align with triangle GHE. This will ensure that the corresponding sides and angles of the two triangles match.

3. Reflection: Reflect the rotated triangle about the x-axis to complete the congruence transformation. This will ensure that the corresponding points of the two triangles are perfectly overlapped.

After these three transformations - translation, rotation, and reflection - triangle ABC will be congruent to triangle GHE.