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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.

Answer 1

To prove that triangle ABC is congruent to triangle GHE, we can use the sequence of transformations:

1. Translation: Shift triangle ABC to the left by 3 units and down by 4 units. This would place point A(1, -3) at point G(-2, 2).

2. Reflection: Reflect triangle ABC over the y-axis. This would change side BC to side HE and side AC to side HG.

3. Translation: Shift the reflected triangle GBC to the left by 3 units and up by 3 units. This would place point G(-2, 2) at point E(-5, 5).

By performing these transformations, triangle ABC would be congruent to triangle GHE, as they would have the same shape and size.