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 (such as rotation) preserve the lengths of the sides of a figure. That is, if \(\triangle ABC\) is rotated to get \(\triangle EFD\), then \(\triangle ABC\cong\triangle EFD\) (by the definition of rotation as a congruence transformation).

Step2: Use the congruence of triangles

For congruent triangles \(\triangle ABC\) and \(\triangle EFD\), the corresponding sides are equal. In congruent triangles, \(CB\) corresponds to \(EF\) (by observing the structure of the two triangles formed by rotation).
Since \(EF = 4.2\) cm and \(CB=EF\) (because of triangle congruence from rotation), we can conclude that \(CB = 4.2\) cm.

Answer:

C. \(4.2\) cm