Question

triangle rst is rotated 180° about the origin, and then translated up 3 units. which congruency statement describes the figures? △rst≅△abc △rst≅△acb △rst≅△bca △rst≅△bac

Explanation:

Step1: Recall transformation properties

Rotations and translations are rigid - motions. Rigid - motions preserve the shape and size of a figure, which means the pre - image and the image are congruent. The order of the vertices in the congruence statement should match the corresponding vertices.

Step2: Identify corresponding vertices

When a triangle is rotated 180° about the origin and then translated, we can match the vertices by observing their relative positions. By visual inspection, we can see that \(R\) corresponds to \(A\), \(S\) corresponds to \(B\), and \(T\) corresponds to \(C\). So the congruence statement is \(\triangle RST\cong\triangle ABC\).

Answer:

A. \(\triangle RST\cong\triangle ABC\)