To demonstrate the congruence of triangle ABC (with vertices A(1, -3), B(1, -1), and C(4, -3)) and triangle GHE (with vertices G(-2, 2), H(-4, 2), and E(-2, 5)), a sequence of transformations can be applied: first, translate triangle ABC left by 3 units and up by 1 unit to align vertex A to point G, and then perform a reflection over the line y = 2 to map the remaining vertices accordingly, proving that △ABC is congruent to △GHE.
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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.
(2 points)
1 answer