Question

the triangles are congruent by sss or hl. the diagram shows the sequence of three rigid transformations used to map \\( \triangle abc \\) onto \\( \triangle a^{\prime \prime}b^{\prime \prime}c^{\prime \prime} \\). what is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation

Explanation:

• First, observe the transformation from \(\triangle ABC\) to \(\triangle A'B'C'\). The orientation of the triangle changes, which is characteristic of a rotation.
• Then, from \(\triangle A'B'C'\) to the intermediate - step (before the final \(\triangle A''B''C''\)), the orientation changes again in a non - translational and non - rotational way (a flip), which is a reflection.
• Finally, from the intermediate - step triangle to \(\triangle A''B''C''\), the position of the triangle changes without change in orientation or shape, which is a translation.

Answer:

rotation, then reflection, then translation