Question

33. In the figure, AO = CO, BO = DO, and Aangle AOD=
90°. Then by SAS postulate​

Answer 1

Step-by-step explanation:

Since the angles opposite to equal sides are equal,

∴AB=AC

⇒∠C=∠B

⇒ 2

∠B = 2∠C.

Since BO and CO are bisectors of ∠B and ∠C, we also have

∠ABO= 2

∠B and ∠ACO= 2∠C

.∠ABO= 2

∠B= 2

∠C =∠ACO.

Consider △BCO:

∠OBC=∠OCB

⇒BO=CO ....... [Sides opposite to equal angles are equal]

Finally, consider triangles ABO and ACO.

BA=CA ...... (given);

BO=CO ...... (proved);

∠ABO=∠ACO (proved).

Hence, by S.A.S postulate

△ABO≅△ACO

⇒∠BAO=∠CAO⇒AO bisects ∠A.