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 requires two sides and the included angle of one triangle to be congruent to the corresponding two sides and included angle of another triangle.

Step2: Analyze the given triangles $\triangle STU$ and $\triangle VTU$

We know that $TU$ is a common side for both triangles.

Step3: Check each option

• Option 1: $UV = 14$ ft and $m\angle TUV=45^{\circ}$ gives information about $\triangle TUV$ but not relevant for the sides and included - angle between $\triangle STU$ and $\triangle VTU$ for SAS.
• Option 2: $TU = 26$ ft just states the length of the common side, but we need more for SAS.
• Option 3: $m\angle STU = 37^{\circ}$ and $m\angle VTU = 37^{\circ}$ gives the included angle between the common side $TU$ and another side for each triangle. If we know the lengths of the corresponding sides adjacent to these angles and the equality of the angles, we can use SAS. This is a valid option.
• Option 4: $ST = 20$ ft, $UV = 14$ ft, and $m\angle UST = 98^{\circ}$ does not give the correct combination of sides and included angle for $\triangle STU$ and $\triangle VTU$ for SAS.
• Option 5: $m\angle UST = 98^{\circ}$ and $m\angle TUV = 45^{\circ}$ gives non - relevant angle information for SAS between $\triangle STU$ and $\triangle VTU$.

Answer:

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