CameraIcon

CameraIcon

SearchIcon

MyQuestionIcon

MyQuestionIcon

ABCD is a qua...

Question

$A B C D$ is a quadrilateral in which $A D = B C$ and $∠ D A B = ∠ C B A$ prove that
$∠ A B D = ∠ B A C$

Open in App

Solution

To Prove : $Δ A B D ≅$ $Δ B A C$
Proof: In quadrilateral $A B C D$ , $A D = B C$ and $∠ D A B = ∠ C B A$

In $Δ A B D$ and $Δ B A C$ , we have
$A D = B C$ Given
$∠ D A B = ∠ C B A$ (given)
$A B = A B$ (common)
$Δ A B D ≅ Δ B A C$ . [ by SAS congurency]
Since $Δ A B D ≅ Δ B A C$ ,
$∠ A B D = ∠ B A C$ [CPCT]

Suggest Corrections

thumbs-up

1

mid-banner-image

mid-banner-image

Similar questions

Q. ABCD is a quadrilateral in which

A D = B C

∠ D A B = ∠ C B A

. Prove that,
(i)

△ A B D ≅ △ B A C

B D = A C

∠ A B D = ∠ B A C

Q. ABCD is a quadrilateral in which AD = BC and

∠ D A B = ∠ C B A

(See the given figure). Prove that

∠ A B D = ∠ B A C .

$A B C D$ is a quadrilateral in which $A D = B C$ and $∠ D A B = ∠ C B A$ . Prove that $∠ A B D = ∠ B A C$ .

A B C D

is a quadrilateral in which

A D = B C

∠ D A B = ∠ C B A

Δ A B D ≅ Δ B A C

B D = A C

∠ A B D = ∠ B A C

Q. Question 2 (iii)
ABCD is a quadrilateral in which AD = BC and

∠ D A B = ∠ C B A

(See the given figure). Prove that

∠ A B D = ∠ B A C .

View More

similar_icon

Related Videos

lock

Introduction to Quadrilaterals

MATHEMATICS

Watch in App

Explore more

Standard VI Mathematics