SOLUTION: Please help me with this proof: Given circle O with diameters AB and DC Prove triangle AOC is congruent to triangle DOB

Algebra ->  Geometry-proofs -> SOLUTION: Please help me with this proof: Given circle O with diameters AB and DC Prove triangle AOC is congruent to triangle DOB      Log On


   

Question 199566: Please help me with this proof:
Given circle O with diameters AB and DC
Prove triangle AOC is congruent to triangle DOB
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the circle with diameters AB and DC. Draw segments AC and BD.
Proof (you may want to state the reasons more formally):
  1. Segments AB and DC are diameters of circle O. Reason : Given
  2. Segments AB and DC pass through the center O. Reason: Definition of diameters
  3. Segments OA, OB, OC and OD are all radii. Reason: Definition of radius
  4. Segments OA, OB, OC and OD are all equal in length. Reason: Definition of circle
  5. Segments OA is congruent to segment OD and segment OC is congruent to segment OB. Reason: Definition of congruent segments<.li>
  6. Angle AOC and angle DOB are vertical angles. Reason: definition of vertical angles.
  7. Angle AOC and angle DOB are congruent. Reason: Vertical angles are congruent
  8. Triangle AOC is congruent to triangle DOB. Reason SAS