Question

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

Explanation:

Step1: Recall SAS (Side - Angle - Side) criterion

SAS congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze each option

• Option 1: Given \(UV = 14\) ft and \(m\angle TUV=45^{\circ}\), we don't have information about the corresponding sides and included - angle in \(\triangle STU\) related to these values for a SAS comparison.
• Option 2: Given \(TU = 26\) ft, we have no information about the corresponding side in \(\triangle STU\) and no included - angle information related to this side for SAS.
• Option 3: If \(m\angle STU = 37^{\circ}\) and \(m\angle VTU=37^{\circ}\), and we know that \(TU\) is common to both \(\triangle STU\) and \(\triangle VTU\). Also, we can consider the sides adjacent to these angles. For example, if we assume some side - length relationships (not given in the problem but conceptually), this gives us the included - angle equality for SAS.
• Option 4: Given \(ST = 20\) ft, \(UV = 14\) ft, and \(m\angle UST = 98^{\circ}\), we don't have the correct combination of sides and included - angle for SAS between \(\triangle STU\) and \(\triangle VTU\).
• Option 5: Given \(m\angle UST = 98^{\circ}\) and \(m\angle TUV = 45^{\circ}\), we don't have the correct side - angle - side combination for SAS between \(\triangle STU\) and \(\triangle VTU\).

Answer:

\(m\angle STU = 37^{\circ}\) and \(m\angle VTU = 37^{\circ}\)