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: Understand the properties of rotation and translation

Rotation and translation are rigid transformations. Rigid transformations preserve the shape and size of the figure. So, the pre - image (triangle \(RST\)) and the image (triangle \(ABC\)) are congruent.

Step2: Check the correspondence of vertices

When we rotate \(\triangle RST\) \(180^{\circ}\) about the origin and translate it up \(3\) units, we need to match the vertices.

• The order of vertices in the congruence statement should correspond.
• By observing the positions of the vertices after transformation, we can see that \(R\) corresponds to \(A\), \(S\) corresponds to \(C\), and \(T\) corresponds to \(B\). But in congruence statements, we can also note that \(\triangle RST\) and \(\triangle ACB\) have the correct vertex - to - vertex correspondence.

Answer:

\(\triangle RST\cong\triangle ACB\)