Question

Q. ABC is an Isosceles Triangle with AB = AC, the Bisector of ∠B and ∠C intersect each other at O. Join A to O.

Show that -
(i) OB = OC
(ii) AC bisects ∠A​

Answer 1

Step-by-step explanation:

(i) In △ABC, we have

AB=AC

⇒∠C=∠B ∣ Since angles opposite to equal sides are equal

$⇒ \frac{1}{2} ∠B=\frac{1}{2} ∠C$

⇒∠OBC=∠OCB

⇒∠ABO=∠ACO …(1)

⇒OB=OC ∣ Since sides opp. to equal ∠s are equal …(2)

(ii) Now, in △ABO and △ACO, we have

AB=AC ∣ Given

∠ABO=∠ACO ∣ From (1)

OB=OC ∣ From (2)

∴ By SAS criterion of congruence, we have

△ABO≅△ACO

⇒∠BAO=∠CAO ∣ Since corresponding parts of congruent triangles are equal

⇒ AO bisects ∠A

Answer 2

Answer:

proved

Step-by-step explanation:

please check my solution is right or wrong