Question

AD and BC are equal and perpendicular to a line segment AB Show that CD bisects AB .​

Answer 1

Step-by-step explanation:

ANSWER

Its given that AD=BC....(i)

AD is perpendicular to AB i.e, ∠OAD=90

o

BC is perpendicular to AB i.e, ∠OBC=90

o

We have to prove that CD bisects AB i.e OA=OB

Since line CD and AB intersect,

∠AOD=∠BOC [vertically opposite angle]....(ii)

In △BOC and △AOD,

∠BOC=∠AOD [from (ii)]

∠CBO=∠DAO [both angles are 90

o

]

⇒BC=AD

∴△BOC≅△AOD [AAS Congruence Rule]

∴BO=AO [CPCT]

Hence CD bisects AB.