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 two sides and the included angle of another triangle.

Step2: Analyze option 1

If $UV = 14$ ft and $m\angle TUV=45^{\circ}$, we already know $SU = 14$ ft from the figure. If we consider $\triangle STU$ and $\triangle VTU$, $SU = UV$, and if we can show the included angles are equal and the other - side is common ($TU$ is common to both triangles), it can be used for SAS.

Step3: Analyze option 2

Just knowing $TU = 26$ ft only gives information about one side. We need two sides and the included - angle, so this is not enough for SAS.

Step4: Analyze option 3

If $m\angle STU = 37^{\circ}$ and $m\angle VTU = 37^{\circ}$, and we know $TU$ is common to both $\triangle STU$ and $\triangle VTU$. Also, if we can show the adjacent sides are equal, it can be used for SAS.

Step5: Analyze option 4

The angles $\angle UST$ and $\angle TUV$ are not the included angles for the sides $ST$, $TU$ and $UV$, $TU$ respectively. So this information cannot be used for SAS.

Step6: Analyze option 5

The angles $\angle UST$ and $\angle TUV$ are not the included angles for the relevant sides in $\triangle STU$ and $\triangle VTU$ for SAS, so this is not useful.

Answer:

UV = 14 ft and $m\angle TUV = 45^{\circ}$, $m\angle STU = 37^{\circ}$ and $m\angle VTU = 37^{\circ}$