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In figure, AC=BD. Prove that angle OAB=angle OCD.
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In triangles
segOC=segOB radii of the same circle
segOA=segOD radii of the same circle
chordAC=chordBD given
so
triangle AOC is congruent triangleDOB SSS test
Now
angle OAB=angle OCD C.A.C.T
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Answer:
In AOC and BOD
AC = BD ( given )
OA = OD ( radii )
OC = OB ( radii )
Therefore, AOC ≅ BOD ( SSS rule )
Therefore, angle AOC = angle BOD ( CPCT )
angle AOC + angle BOC = angle BOD + angle BOC ( since angle AOC = angle BOD )
Therefore, angle AOB = angle COD
In AOB and COD,
OA = OB ( radii )
angle AOB = angle COD ( proved above )
OC = OD ( radii )
Therefore, AOB ≅ COD ( SAS rule )
Therefore, angle OAB = angle OCD ( CPCT )
Step-by-step explanation:
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