Question

triangle rst is rotated 180° about the origin, and then translated up 3 units. which congruency statement describes the figures?
○ δrst ≅ δacb
○ δrst ≅ δabc
○ δrst ≅ δbca
○ δrst ≅ δbac

Explanation:

Rotation and translation are rigid transformations. Rigid transformations preserve the shape and size of the figure, so the pre - image and the image are congruent. We need to check the correspondence of vertices.
When we consider the congruence statement, the order of vertices in the congruence statement should match the correspondence of the congruent triangles.
For \(\triangle RST\) and \(\triangle ABC\), after rotation and translation, the vertices \(R\) corresponds to \(A\), \(S\) corresponds to \(B\), and \(T\) corresponds to \(C\).

Answer:

\(\triangle RST\cong\triangle ABC\)