Question

triangle qrs and triangle fgs are drawn below. if $overline{qs}congoverline{fs},overline{qr}congoverline{fg}$, and $overline{rs}congoverline{gs}$, use the dropdown boxes below to determine a transformation that maps triangle qrs onto triangle fgs. then use a congruence statement to explain why this is possible.

Explanation:

Step1: Identify transformation type

A rotation about point S will map △QRS onto △FGS.

Step2: Apply congruence criterion

Since $\overline{QS}\cong\overline{FS}$, $\overline{QR}\cong\overline{FG}$, and $\overline{RS}\cong\overline{GS}$, by the Side - Side - Side (SSS) congruence criterion, $\triangle QRS\cong\triangle FGS$. The rotation about point S is possible because the two triangles are congruent, and corresponding vertices can be made to coincide through this rigid - motion transformation.

Answer:

A rotation about point S maps △QRS onto △FGS because △QRS≅△FGS by SSS.