Use rigid motions to show triangle congruence through corresponding sides and angles.
Use a coordinate transformation to prove triangle congruence
Problem
Apply \(T(x,y)=(x+2,y-3)\) to \(A(0,0)\), \(B(3,0)\), \(C(0,4)\), whose proposed corresponding image is \(D(2,-3)\), \(E(5,-3)\), \(F(2,1)\). Identify the transformation, give \(\text{all}~\text{three}~\text{image}~\text{vertices}\), and determine whether \(\triangle~ABC~\cong~\triangle~DEF\).
Treat the coordinate rule as one motion acting on the entire triangle, not as three unrelated calculations. Compare the displacement from each original vertex to its proposed partner, make sure the same change works every time, and then use the fact that a translation is rigid to connect the mapping to congruence.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
