Question

during geometry class, students are told that δtsr ≅ δusv. marcus states that δtsr is mapped to δusv by performing a rotation about point s. sam states that δtsr is mapped to δusv 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 manner around S. But observing the orientation of △TSR and △USV, a rotation about S will not map △TSR onto △USV as the corresponding sides and angles will not align correctly.

Step2: Analyze reflection

If we consider the line passing through point S, we can see that reflecting △TSR across this line will map it onto △USV. The corresponding vertices T and U, R and V, and the shared vertex S will match up correctly when a reflection is performed across the appropriate line through S.

Answer:

Sam is correct.