To show that triangle \( ABC \) is congruent to triangle \( GHE \), we can use a sequence of transformations. First, we can perform a translation by moving triangle \( ABC \) from its original position to align point \( A(1, -3) \) to point \( G(-2, 5) \). This translation vector is \( <-3, 8> \). Next, we can apply a rotation about point \( G(-2, 5) \) that aligns side \( AB \) with side \( GH \) and points \( B(1, -1) \) to \( H(-4, 2) \). Finally, we can apply a reflection across the line perpendicular to \( GH \) that passes through point \( G \). This sequence of transformations—translation, rotation, and reflection—demonstrates that the two triangles are congruent.
A(1,-3)
B(1,-1)
C(4,-3)
E(-2,5)
H(-4,2)
E(-2,5)
△ABC is congruent to △GHE. Describe a sequence of transformations from △ABC to △GHE that proves their congruence in a short paragraph
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