Use rigid motions to show triangle congruence through corresponding sides and angles.
Give a rigid-motion sequence mapping one triangle to another
Problem
Infer the unique motion from this allowed one-step family: translations, reflections across the coordinate axes, and \(90°/180°/270°\) rotations about the origin. It maps \(A(0,0)\to~D(4,1)\), \(B(3,0)\to~E(7,1)\), and \(C(0,2)\to~F(4,3)\).
Infer the rigid motion from coordinate patterns across the entire correspondence. Compute target minus source for all three vertex pairs and compare those results with the sign-change and swap patterns of the other allowed motions; only a rule that passes every labeled pair maps the whole triangle.
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