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, ABC and EGH, are plotted on the graph. The triangle ABC has its vertices marked with closed points at A(1, -3), B (1, -1), and C (4, -3).
The triangle EGH has its vertices marked with closed points at E (-2, 5), G (-2, 2), and H (-4, 2). In triangle EGH, side EG is labeled as h, side GH is labeled as e, and side HE is labeled as g.
△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to △GHE that proves their congruence.
The sequence of transformations from triangle ABC to triangle GHE that proves their congruence is as follows:
1. Translation: Triangle ABC is translated 3 units left and 4 units up to map onto triangle EGH. This means that all corresponding vertices of triangle ABC are now in the same position as the vertices of triangle GHE.
2. Rotation: A 180 degree rotation is then applied to triangle ABC around the point of intersection of segments AG and EH. This rotation would map triangle ABC perfectly onto triangle GHE, confirming their congruence.