Asked by j

The frame of a bridge is constructed of triangles, as shown below.

A large triangle is made up of 4 smaller triangles within the larger triangle. Vertical line T U cuts the large triangle in half. Lines U S and U V are diagonal from point U and go up to each side. Angle S U T is 45 degrees and angle T V U is 98 degrees. Line segment T V is 20 feet and line segment S U is 14 feet.
What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

UV = 14 ft and m∠TUV = 45°
TU = 26 ft
m∠STU = 37° and m∠VTU = 37°
ST = 20 ft, UV = 14 ft, and m∠UST = 98°
m∠UST = 98° and m ∠TUV = 45°

All Answers 1

Answered by GPT-5 mini AI
Answer: (1) UV = 14 ft and m∠TUV = 45°; and (4) ST = 20 ft, UV = 14 ft, and m∠UST = 98°.

Reason: TU is common.
- (1) gives SU = UV (both 14) and the included angles at U equal (45°), so SAS.
- (4) (together with the given TV = 20 and SU = 14 and given m∠TVU = 98°) gives ST = TV and SU = UV and the included angles at S and V equal (98°), so SAS.