Answer:-The first and fourth information can be the additional information to show that ΔSTU ≅ ΔVTU by SAS.
Explanation:-
Given :- In ΔSTU and ΔVTU
SU=14ft , VT=20 ft ,m∠SUT=45° and m∠TUV=98°
The given additional information:-
1.UV = 14 ft and m∠TUV = 45°
Then SU=UV = 14 ft [given]
m∠TUV =m ∠SUT=45° [given]
TU=TU [Reflexive property]
⇒ΔSTU ≅ ΔVTU [SAS congruence postulate]
2. TU = 26 ft
⇒ Not enough information to prove triangles congruent.
3. m∠STU = 37° and m∠VTU = 37°
⇒m∠STU = 37° =m∠VTU = 37° [Transitive property]
And TU=TU[Reflexive property]
But we need one more information to prove them congruent.
4. ST = 20 ft, UV = 14 ft, and m∠UST = 98°
ST = 20 ft=TV [given]
m∠UST = 98°=m∠UVT [given]
TU=TU [Reflexive property]
⇒ΔSTU ≅ ΔVTU [ SAS postulate]
5. m∠UST = 98° and m ∠TUV = 45°
m∠UST = 98°=m∠UVT [given]
TU=TU [Reflexive property]
m ∠TUV = 45°=∠TUS [given]
⇒ΔSTU ≅ ΔVTU [AAS congruence theorem]
Thus the first and fourth information can be the additional information to show that ΔSTU ≅ ΔVTU by SAS.
