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Standard IX

Mathematics

Isosceles Triangle Property

Question 1 iI...

Question

Question 1 (i)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C i n t e r s e c t$
each other at O. Join A to O. Show that:
OB = OC

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Solution

$I t i s g i v e n t h a t A B = A C t h e r e f o r e, ∠ B = ∠ C (A n g l e s o p p o s i t e t o e q u a l s i d e s a r e e q u a l) \Rightarrow \frac{1}{2} (∠ B) = \frac{1}{2} (∠ C) \Rightarrow ∠ O B C = ∠ O C B (O B a n d O C a r e b i s e c t o r s o f ∠ B a n d a n d ∠ C) T h e r e f o r e, O B = O C (S i d e s o p p o s i t e t o e q u a l a n g l e s a r e e q u a l)$

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Similar questions

Question 1 (i)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C i n t e r s e c t$
each other at O. Join A to O. Show that:
OB = OC

Q. In an isosceles triangle

A B C

, with

A B = A C

, the bisectors of

∠ B

and

∠ C

intersect each other

O

. Join

A

O

. Show that:

O B = O C

Question 1 (ii)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C$ intersect each other at O. Join A to O. Show that:
AO bisects $∠ A$

Question 1 (ii)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C$ intersect each other at O. Join A to O. Show that:
AO bisects $∠ A$

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

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Isosceles Triangle Property

Standard IX Mathematics

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Question 1 (i) 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: OB = OC

It is given that AB=ACtherefore,∠B=∠C (Angles opposite to equal sides are equal)⇒12(∠B)=12(∠C)⇒∠ OBC=∠ OCB (OB and OC are bisectors of ∠ B and and ∠ C)Therefore, OB=OC (Sides opposite to equal angles are equal)

Question 1 (i)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C i n t e r s e c t$
each other at O. Join A to O. Show that:
OB = OC