You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Congruency Postulates

In an isoscel...

Question

In an isosceles triangle $A B C$ , with $A B = A C$ , the bisectors of $∠ B$ and $∠ C$ intersect each other $O$ . Join $A$ to $O$ . Show that $A O$ bisects $∠ A$

Open in App

Solution

To prove:
$∠ O A B = ∠ O A C$
$O B = O C$ ............(1)
Also, in $Δ A B O$ and $Δ A C O$ , we have
$A B = A C$ (Given)
$A O = A O$ (Common)
$O B = O C$ (From(1))
$∴ Δ A B O ≅ Δ A C O$ (SSS congruence rule)
$\Rightarrow ∠ O A B = ∠ O A C$ (CPCT)
Hence proved

Suggest Corrections

Similar questions

Q. In an isosceles triangle

A B C

, with

A B = A C

, the bisectors of

∠ B

and

∠ C

intersect each other at

O

. Join

A

O

. Show that :
(i)

O B = O C

(ii)

A O

bisects

∠ A

In an isosceles triangle $A B C$ , with $A B = A C$ ,the bisectors of $∠ B$ and $∠ C$ interest each other at $O$ .join $A$ to $O$ show that:
(i) $O B = O C$
(ii) $A O$ 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 $∠ A$

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 $∠ A$

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

Join BYJU'S Learning Program

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

To prove:∠OAB=∠OACOB=OC ............(1)Also, in ΔABO and ΔACO, we haveAB=AC (Given)AO=AO (Common)OB=OC (From(1))∴ΔABO≅ΔACO (SSS congruence rule)⇒∠OAB=∠OAC (CPCT)Hence proved

In an isosceles triangle $A B C$ , with $A B = A C$ , the bisectors of $∠ B$ and $∠ C$ intersect each other $O$ . Join $A$ to $O$ . Show that $A O$ bisects $∠ A$

To prove:
$∠ O A B = ∠ O A C$
$O B = O C$ ............(1)
Also, in $Δ A B O$ and $Δ A C O$ , we have
$A B = A C$ (Given)
$A O = A O$ (Common)
$O B = O C$ (From(1))
$∴ Δ A B O ≅ Δ A C O$ (SSS congruence rule)
$\Rightarrow ∠ O A B = ∠ O A C$ (CPCT)
Hence proved