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Answer:
BO=AO
Step-by-step explanation:
Given:
AD=BC (1st equation)
AD perpendicular to AB , i.e. angle OAD= 90°
BC perpendicular to AB , i.e. angle OBC=90°
TO PROVE: CD bisects AB i.e. OA=OB
PROOF:
Since,
Line CD & AB intersect
Angle AOD =Angle BOC (vertically opposite angles) -2nd equation
In ∆BOC and ∆AOD,
Angle BOC = Angle AOD ( from equation 2)
Angle CBO = Angle DAO (both angles are 90°)
BC=AD (from equation 1)
Therefore, ∆BOC Congruence to ∆AOD (AAS Congruence rule)
therefore, BO=AO
Hence porved