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 = 3.8 cm, and de = 4.5 cm, what is cb?
○ 3.3 cm
○ 3.8 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 the figure. That is, if triangle \(ABC\) is rotated to get triangle \(EFD\), then \(\triangle ABC\cong\triangle EFD\).

Step2: Identify the corresponding sides

In congruent triangles \(\triangle ABC\) and \(\triangle EFD\), the side \(CB\) corresponds to the side \(EF\).

Answer:

C. \(4.2\) cm