Congruency of Triangles Quick Check 5 of 55 of 5 Items Question Use the image to answer the question. To prove the triangles are congruent, which of the following rigid motions would map △GHJ to △ZNP ? (1 point) Responses translation along the vector, mapping point J to point P, then rotation −90° (clockwise) about point J translation along the vector, mapping point upper J to point upper P , then rotation negative 90 degrees (clockwise) about point upper J rotation −90° (clockwise) about point J, then translation along the vector, mapping point H to point Z rotation negative 90 degrees (clockwise) about point upper J , then translation along the vector, mapping point upper H to point upper Z translation along the vector, mapping point G to point N, then rotation −90° (clockwise) about point G translation along the vector, mapping point upper G to point upper N , then rotation negative 90 degrees (clockwise) about point upper G translation along the vector, mapping point J to point P, then rotation 90° (counterclockwise) about point J translation along the vector, mapping point upper J to point upper P , then rotation 90 degrees (counterclockwise) about point upper J Skip to navigation page 9 of 9 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the rigid motions that would map triangle \( \triangle GHJ \) to triangle \( \triangle ZNP \), we need to examine the corresponding points and their positions.

1. Identify Corresponding Points:

   • Point \( G \) should correspond to point \( N \).
   • Point \( H \) should correspond to point \( Z \).
   • Point \( J \) should correspond to point \( P \).

2. Analyze the Proposed Rigid Motions:

   • Rigid motions include translations and rotations, both of which maintain the shape and size of the triangles.

3. Check Each Option:

   • Translation along the vector from \( J \) to \( P \), then a rotation -90° (clockwise) about \( J \): This first translates \( J \) to \( P \), not matching the other points.
   • Rotation -90° (clockwise) about \( J \), then translation from \( H \) to \( Z \): You're rotating around \( J \) and then translating, which could potentially match but needs to be verified with the actual positions.
   • Translation from \( G \) to \( N \), then rotation -90° (clockwise) about \( G \): This would place \( G \) in the position of \( N \) but doesn’t take into account the others correctly.
   • Any translations and rotations that don't maintain the point correspondence or order will not work.

4. Find the Correct Mapping:

   • When using the combination of translations and rotations, identify if the triangles correspond in a manner that respects the distance and angles.

Without the actual image for visual reference, this analysis is limited, and the ideal answer would depend on comparison with the given points:

To conclude, the best approach is to identify which rigid motions will correctly position each vertex in the corresponding triangle, confirming the triangles' congruency as required. If there is still uncertainty or multiple options seem plausible, further checking with the visual image provided would be essential for the correct choice.