In order to determine the type of rigid transformation that maps triangle \( \triangle GHI \) onto triangle \( \triangle JKL \), we first need the coordinates of the vertices for both triangles.
Assuming we have the coordinates for \( \triangle GHI \) as \( G(x_1, y_1) \), \( H(x_2, y_2) \), and \( I(x_3, y_3) \) and for \( \triangle JKL \) as \( J(a_1, b_1) \), \( K(a_2, b_2) \), and \( L(a_3, b_3) \), we can proceed with the following steps:
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Translation: Check if there is a translation vector \( (d_x, d_y) \) such that translating \( \triangle GHI \) moves it to the position of \( \triangle JKL \). This is calculated by checking if: \[ J = G + (d_x, d_y), K = H + (d_x, d_y), L = I + (d_x, d_y) \]
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Rotation: If translation is not sufficient, we can consider rotation. Two triangles can be related by a rotation if their corresponding angles are equal and the sides are proportional in length.
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Reflection: Lastly, check for reflection. If the two triangles are congruent but have opposite orientations, then a reflection could be the transformation that maps one triangle onto the other.
To specifically find out which transformation works, you can compute the distances between corresponding vertices and angles. If the distances remain the same under a translation and the angles are preserved, then it is a translation. If only the angles match, it may be a rotation or reflection.
If you provide the specific coordinates of the triangles, I can help you determine the exact rigid transformation.