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:

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 vertices in a congruency statement must match the corresponding vertices.

Step2: Identify corresponding vertices

When \(\triangle RST\) is rotated \(180^{\circ}\) about the origin and then translated up 3 units, we need to match the vertices. By observing the orientation and position of the triangles, we can see that \(R\) corresponds to \(B\), \(S\) corresponds to \(A\), and \(T\) corresponds to \(C\). So the correct congruency statement is \(\triangle RST\cong\triangle BAC\).

Answer:

\(\triangle RST\cong\triangle BAC\)