What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

I think the correct solutions are: UV = 14 ft and m∠TUV = 45°; ST = 20 ft, UV = 14 ft, and m∠UST = 98°. In other words, Options A and D.

The initial and fourth pieces of information can serve as supplemental details to demonstrate that ΔSTU ≅ ΔVTU using SAS. To explain, in ΔSTU and ΔVTU, we have SU=14ft, VT=20 ft, m∠SUT=45°, and m∠TUV=98°. The additional information provided is: 1. UV = 14 ft and m∠TUV = 45°, thus SU=UV = 14 ft [given], and m∠TUV = m∠SUT = 45° [given]. The length TU is the same in both triangles due to the Reflexive property, resulting in ΔSTU ≅ ΔVTU via the SAS congruence postulate. 2. TU = 26 ft, which does not provide sufficient information to establish triangle congruence. 3. m∠STU = 37° and m∠VTU = 37°, meaning we also need additional data to confirm their congruency. 4. ST = 20 ft, UV = 14 ft, and m∠UST = 98° leads to ST = 20 ft=TV [given], and the reflexive property shows TU=TU, thus establishing ΔSTU ≅ ΔVTU under the SAS postulate. 5. m∠UST = 98° alongside m∠TUV = 45° also supports ΔSTU ≅ ΔVTU through the AAS congruence theorem. Therefore, the first and fourth pieces of information can indeed serve to demonstrate that ΔSTU ≅ ΔVTU using SAS.