Question

in the adjoining figure, OA bisects angle A and angle ABO is equal to angle OCA. Prove that OB is equal to OC (hint : OAB congruent to OAC, ASA property)

Answer 1

Answer:

The sides OB and OC are equal by CPCTC.

Step-by-step explanation:

Given information: OA bisects angle A, $\angle ABO=\angle OCA$

In triangle OAB and OBC,

$\angle ABO=\angle OCA$                (Given)

$\angle OAB=\angle OAC$                (OA bisects angle A)

$OA=OA$                                             (Common side)

By AAS postulate,

$\triangle OAB\cong \triangle OAC$

Since corresponding parts of congruent triangles are congruent, therefore

$OB=OC$                              (CPCTC)

Hence proved.

Answer 2

Answer:

The sides OB and OC are equal by CPCT

Step-by-step explanation:

Given  OA bisects angle A. we have to prove that OB=OC

In triangle OAB and OAC,

∠ABO=∠ACO     (∵Given)

∠BAO=∠CAO     (∵OA bisects angle A)

AO=AO               (∵Common side)

By AAS postulate, ΔOAB≅ΔOAC

Since corresponding parts of congruent triangles are congruent

∴ By CPCT, OB=OC

Hence proved.