Question

triangle abc is rotated 45° about point x, resulting in triangle efd.
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
figure may not be drawn to scale

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, \(\triangle ABC\cong\triangle EFD\) (by the property of rotation).

Step2: Identify corresponding sides

In congruent triangles \(\triangle ABC\) and \(\triangle EFD\), the corresponding sides are equal. That is, \(CB = DF\).

Answer:

\(3.6\mathrm{cm}\) (the second option)