Question

The frame of a bridge is constructed of triangles, as shown additional information could you use to show that δstu ≅ δvtu using sas? check all that apply.

1. uv = 14 ft and m∠tuv = 45°
2. tu = 26 ftm∠stu = 37° and m∠vtu = 37°
3. st = 20 ft, uv = 14 ft, and m∠ust = 98°
4. m∠ust = 98° and m ∠tuv = 45°

Answer 1

To prove ΔSTU ≅ ΔVTU using SAS, you need two sides and the included angle of the triangles to be congruent. The only information that provides this is option 2, which gives equal angles and a common side, fulfilling the SAS criteria.

Step-by-step explanation:

To show that ΔSTU ≅ ΔVTU using the SAS (Side-Angle-Side) congruence theorem, you need to establish that one pair of corresponding sides is equal in length, the angle between them is equal, and the other pair of corresponding sides of the triangles are equal in length.

The following information would suffice:

• TU = 26 ft, m∠STU = 37°, and m∠VTU = 37°: This information provides equal angles between sides ST and TU, and VT and TU, and a common side TU, fulfilling the SAS criteria.
• UV = 14 ft and m∠TUV = 45°: This does not provide sufficient information for SAS as there is no information about the sides TU connected to angle TUV.
• ST = 20 ft, UV = 14 ft, and m∠UST = 98°: This information does not apply to SAS for triangles STU and VTU since side UV is not part of triangle STU.
• M∠UST = 98° and m∠TUV = 45°: This does not provide two sides and the included angle between those sides for either triangle STU or VTU.

Thus, the most relevant piece of information to prove congruence by SAS is the pair of equal angles and the common side TU, as given in option 2.