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.

Question

△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to  △GHE that proves their congruence. 50 word limit

Answer 1

To show that triangle \(ABC\) is congruent to triangle \(GHE\), first translate triangle \(ABC\) downwards by 5 units to align point \(A\) with point \(E\). Then, reflect the translated triangle over the vertical line \(x = -2\) to match the orientation and location of triangle \(GHE\).