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. do it shorter

Answer 1

To demonstrate the congruence of triangles \( \triangle ABC \) and \( \triangle GHE \) through transformations, follow these steps:

1. Translation: Move \( \triangle ABC \) downwards by 5 units and to the left by 3 units. This transformation aligns point \( A(1, -3) \) with point \( E(-2, 5) \).

2. Reflection: Reflect the translated triangle \( \triangle ABC \) across the vertical line \( x = -2 \) to match the orientation of \( \triangle GHE \).

These transformations (translation followed by reflection) show that \( \triangle ABC \cong \triangle GHE \).