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An isosceles $A B C$ , where $A B = A C$ and bisectors of $∠ B$ and $∠ C$ intersect each other at $O$ , then $∠ OAB= ∠ OAC$ .

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True

False

answer is A.

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Detailed Solution

It is given that an isosceles

Δ A B C

, where

A B = A C

and bisectors of

∠ B

and

∠ C

intersect each other at

O

Consider

Δ A B O

and

Δ A C O

from the figure given.

O A = O A

(Common side)

A B = A C

(Given)
Consider

A

as the congruence rule,

A B = A C

.
The angles

∠ B, ∠ C

that are opposite to equal sides are equal.

∠ A C B = ∠ A B C

O B = O C

[Sides opposite to equal angles are equal.]

Δ A O B ≅ Δ A O C

[By SSS congruence criterion]

∠ O A B = ∠ O A C

.
Therefore, by congruent parts of congruent triangles (CPCT),

O B = O C

.
Hence the given statement is true.
Hence option 1 is correct.

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