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? figure may not be drawn to scale.

Explanation:

Step1: Recall rotation property

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve side - lengths and angle - measures. So, if triangle ABC is rotated to form triangle EFD, then triangle ABC and triangle EFD are congruent.

Step2: Identify corresponding sides

In congruent triangles, corresponding sides are equal. By the order of the vertices (triangle ABC and triangle EFD), side CB corresponds to side FE.

Step3: Find the length of CB

Given that EF = 4.2 cm, and CB = EF (corresponding sides of congruent triangles), then CB = 4.2 cm.

Answer:

4.2 cm