Question

1. after a counterclockwise rotation about point x, scalene triangle abc maps onto △rst, as shown in the diagram below. which one of the following statements must be true? a) \\( \overline { c b } = \overline { t r } \\) b) \\( \overline { c a } = \overline { t s } \\) c) \\( \angle a = \angle r \\) d) \\( \angle a = \angle s \\)

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, \(\triangle ABC\cong\triangle RST\).

Step2: Use the congruent - triangle property

If \(\triangle ABC\cong\triangle RST\), then corresponding parts are congruent. That is, \(AB = RS\), \(BC=ST\), \(CA = TR\), \(\angle A=\angle R\), \(\angle B=\angle S\), \(\angle C=\angle T\).

Answer:

C. \(\angle A=\angle R\)