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

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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Geometry proofs Question 199566: Please help me with this proof: Given circle O with diameters AB and DC Prove triangle AOC is congruent to triangle DOBAnswer by jsmallt9(3296)   (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):Segments AB and DC are diameters of circle O. Reason : GivenSegments AB and DC pass through the center O. Reason: Definition of diametersSegments OA, OB, OC and OD are all radii. Reason: Definition of radiusSegments OA, OB, OC and OD are all equal in length. Reason: Definition of circleSegments OA is congruent to segment OD and segment OC is congruent to segment OB. Reason: Definition of congruent segments<.li>Angle AOC and angle DOB are vertical angles. Reason: definition of vertical angles.Angle AOC and angle DOB are congruent. Reason: Vertical angles are congruentTriangle AOC is congruent to triangle DOB. Reason SAS