Question

triangle abc is rotated 45° about point x, resulting in triangle efd. figure may not be drawn to scale if ef = 4.2 cm, df = 3.6 cm, and de = 4.5 cm, what is cb? ○ 3.3 cm ○ 3.6 cm ○ 4.2 cm ○ 4.5 cm

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (rotations, translations, reflections) preserve the lengths of the sides of a figure. So, \(\triangle ABC\cong\triangle EFD\).

Step2: Identify the corresponding sides

In congruent triangles \(\triangle ABC\) and \(\triangle EFD\), \(CB\) corresponds to \(DF\) (by the order of the vertices in the congruence statement \(\triangle ABC\cong\triangle EFD\)).

Answer:

\(3.6\) cm (since \(CB = DF\) and \(DF = 3.6\) cm)