Options
A. UV = 14 ft and m∠TUV = 45°
B. TU = 26 ft
C. m∠STU = 37° and m∠VTU = 37°
D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°
E. m∠UST = 98° and m ∠TUV = 45°
Answer:
A. UV = 14 ft and m∠TUV = 45°
D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°
Step-by-step explanation:
Given
See attachment for triangle
Required
What proves that: ΔSTU ≅ ΔVTU using SAS
To prove their similarity, we must check the corresponding sides and angles of both triangles
First:
[tex]\angle UST[/tex] must equal [tex]\angle UVT[/tex]
So:
[tex]\angle UST = \angle UVT = 98[/tex]
Next:
UV must equal US.
So:
[tex]UV = US = 14[/tex]
Also:
ST must equal VT
So:
[tex]ST = VT = 20[/tex]
Lastly
[tex]\angle TUV[/tex] must equal [tex]\angle TUS[/tex]
So:
[tex]\angle TUV = \angle TUS = 45[/tex]
Hence: Options A and D are correct
