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.
To prove that △ABC is congruent to △GHE, we need to show that the two triangles can be transformed to match each other.
First, we can perform a translation by moving the entire triangle △ABC two units to the left and three units up. This will align point A(1, -3) with point E(-2, 5), point B(1, -1) with point G(-2, 2), and point C(4, -3) with point H(-4, 2).
Next, we can perform a reflection over the x-axis. This will flip the triangle △GHE upside down and make it match the orientation of △ABC.
Finally, we can perform a rotation of 180 degrees about the origin. This will rotate the triangle △GHE while keeping the corresponding points aligned with △ABC.
By performing these transformations, we have shown that △ABC can be transformed into △GHE, proving their congruence.