Question

3. Take any point in the interior of a triangle ABC as shown in the figure.


IS
(a) AO + BO > AB
(c) AO + OC > AC
(b) OB + OC > BC
(d) AB + BC > AC?​

Answer 1

Step-by-step explanation:

please mark me as BRAINLIEST

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:

(i) OB = OC (ii) AO bisects ∠A

Ans. (i) In ΔABC, we have

∴ AB = AC

[Given]

∠C = ∠B

[Angle opposite to equal sides are equal]

or ∠OCB = ∠OBC

⇒ OB = OC

[Sides opposite to equal angles are equal]

(ii) In ΔABO and ΔACO, we have

AB = AC

[Given]

OB = OC

[Proved]

∴ Using SAS criteria,

ΔABO ≌ ΔACO

⇒ ∠OAB = ∠OAC

[c.p.c.t.]

⇒ AO bisects ∠A.