Question

during geometry class, students are told that $delta tsrcongdelta usv$. marcus states that $delta tsr$ is mapped to $delta usv$ by performing a rotation about point s. sam states that $delta tsr$ is mapped to $delta usv$ by a reflection across the line that goes through point s. determine if either student is correct. marcus is correct. sam is correct. both students are correct. neither student is correct.

Explanation:

Step1: Analyze rotation

A rotation about point S would change the orientation of △TSR in a circular - like motion around S. But observing the figure, the orientation of △TSR and △USV is not related by a simple rotation about S.

Step2: Analyze reflection

If we consider the line passing through point S, we can see that the vertices of △TSR and △USV are mirror - images of each other with respect to the line passing through S. For example, point T and point U, point R and point V are symmetric about this line.

Answer:

Sam is correct.