Question

1. triangle abc is congruent to triangle abc.

describe a sequence of rigid motions that takes a to a, b to b,
and c to c.

Explanation:

Step1: Translate triangle ABC

Translate triangle \(ABC\) so that point \(B\) maps to point \(A'\). Let the translation vector be \(\overrightarrow{BA'}\). After translation, the new triangle (let's call it \(A_1B_1C_1\)) has \(B_1 = A'\).

Step2: Rotate the translated triangle

Rotate the translated triangle \(A_1B_1C_1\) around point \(A'\) (which was \(B_1\)) by the angle between \(\overrightarrow{A_1B_1}\) (originally \(\overrightarrow{AB}\)) and \(\overrightarrow{A'B'}\). This rotation will map \(A_1\) to \(B'\) and \(C_1\) to \(C'\)

Answer:

First, translate triangle \(ABC\) by the vector \(\overrightarrow{BA'}\). Then, rotate the translated triangle around point \(A'\) by the angle between \(\overrightarrow{AB}\) (in the original triangle) and \(\overrightarrow{A'B'}\)