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

Byju's Answer

Standard VIII

Mathematics

Construction of Parallel Lines

In the adjoin...

Question

In the adjoining figure, $Δ A B C$ is an isosceles triangle in which $A B = A C .$ Also, $D$ is a point such that $B D = C D$ . Prove that $A D$ bisects $∠ A$ and $∠ D$ .

Open in App

Solution

In $Δ A B C$ and $Δ B C D$
$∠ A B C = ∠ A C B ∠ D B C = ∠ D C B ⟹ ∠ A B D = ∠ A C D$
By $S A S$ criteria
$Δ A B D \sim Δ A C D$
$⟹ ∠ B A D = ∠ D A C ∠ B D A = ∠ A D C$
So $A D$ is angular bisector of $∠ A$ and $∠ B$

Suggest Corrections

Similar questions

Q. In the given figure,

A B C

is an isosceles triangle in which

A B = A D

. Also,

D

is a point such that

B D = C D

. then "

A D

bisects

∠ A

and

∠ D

." is ?

Q. In given figure ABC is an isosceles triangle with AB=AC and D is a point on AC such that

{B C}^{2} = A C \times C D

. Prove that BD=BC.

Δ A B C

is an isosceles triangle such that

A B = A C

, prove that the altitude

A D

from

A

B C

bisects

A B

Q. In the adjoining figure, ∆ABC is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, prove that BE = CF.

Figure

In the given figure, $△ A B C$ is an isosceles triangle in which $A B = A C$ . If $A B$ and $A C$ are produced to $D$ and $E$ respectively such that $B D = C E$ .
Prove that $B E = C D .$

Join BYJU'S Learning Program

In the adjoining figure, ΔABC is an isosceles triangle in whichAB=AC. Also, D is a point such that BD=CD . Prove that AD bisects∠A and ∠D .

In ΔABC and ΔBCD∠ABC=∠ACB∠DBC=∠DCB⟹∠ABD=∠ACDBy SAS criteria ΔABD∼ΔACD⟹∠BAD=∠DAC∠BDA=∠ADCSo AD is angular bisector of ∠A and ∠B

In the adjoining figure, $Δ A B C$ is an isosceles triangle in which $A B = A C .$ Also, $D$ is a point such that $B D = C D$ . Prove that $A D$ bisects $∠ A$ and $∠ D$ .

In $Δ A B C$ and $Δ B C D$
$∠ A B C = ∠ A C B ∠ D B C = ∠ D C B ⟹ ∠ A B D = ∠ A C D$
By $S A S$ criteria
$Δ A B D \sim Δ A C D$
$⟹ ∠ B A D = ∠ D A C ∠ B D A = ∠ A D C$
So $A D$ is angular bisector of $∠ A$ and $∠ B$