In circle E, and are diameters. Angle BCA measures 53°. Circle E is shown. Line segments A C and B D are diameters. Lines are dr
2 answers:
Answer:
Step-by-step explanation:
Givens
- AC and BD are diameters.
- Angle BCA measures 53°.
Notice that line segment BE is congruent to line segment CE, because they are the radius of the circumference. That means the triangle that contains these sides is isosceles.
, by definition of triangles isosceles.
Then,
, by sum of internal angles.
And,
, by vertical angles definition.
But, we know that the measured of a subtended arc is equal to its angle.
Therefore,
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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:
must equal
So:
Next:
UV must equal US.
So:
Also:
ST must equal VT
So:
Lastly
must equal
So:
Hence: Options A and D are correct
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