Use the image to answer the question.

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. Do it in two sentences.

Answer 1

To prove the congruence of triangle \( \triangle ABC \) to triangle \( \triangle GHE \), first perform a reflection across the line \( y = -1 \) to move triangle \( ABC \) into the same orientation as triangle \( GHE \). Next, translate triangle \( ABC \) horizontally to the left by 3 units, aligning it with the position of triangle \( GHE \).