Use rigid motions to show triangle congruence through corresponding sides and angles.
Verify triangle congruence under rotation
Problem
Rotate triangle \(A(1,2)\), \(B(4,2)\), \(C(2,5)\) \(90°\) counterclockwise about the origin. Give the rotation rule, \(\text{all}~\text{three}~\text{image}~\text{vertices}\), congruence result, and orientation change.
For a rotation, lock in the center, turn size, and direction before touching the coordinates; those three features determine one rule for every vertex. After mapping the full triangle, use equal center distances and equal turning angles to justify one rigid motion, while treating congruence and vertex-order behavior as separate conclusions.
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