Question

the frame of a bridge is constructed of triangles as shown. what additional information could you use to show that △stu≅△vtu using sas? choose two correct answers. m∠ust = 98°, st = 20 ft, uv = 14 ft, and m∠stu = 37° and m∠vtu = 37°. uv = 14 ft and m∠tuv = 45°. m∠ust = 98° and m∠tuv = 45°

Explanation:

Step1: Identify SAS requirements

SAS needs two sides and included angle congruent.

Step2: Analyze shared side

△STU and △VTU share TU, so TU≅TU (reflexive).

Step3: Evaluate Option 2

UV=14 ft (VU=SU=14 ft) and ∠TUV=45° (∠VUT=∠SUT=45°). SU≅VU, ∠SUT≅∠VUT, TU≅TU: SAS.

Step4: Evaluate Option 4

m∠STU=37° and m∠VTU=37° (∠STU≅∠VTU). ST=VT=20 ft (given), TU≅TU: SAS.

Answer:

B. UV = 14 ft and m∠TUV = 45°, D. m∠STU = 37° and m∠VTU = 37°