Question

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

Answer 1

I believe the correct answers are:

UV = 14 ft and m∠TUV = 45°
ST = 20 ft, UV = 14 ft, and m∠UST = 98°

Or, in other words, Options A and D.

Answer 2

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.