CameraIcon

CameraIcon

SearchIcon

MyQuestionIcon

MyQuestionIcon

Proof for Validity of Construction of a Perpendicular Bisector

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
(i) $△ A B D ≅ △ B A C$
(ii) $B D = A C$
(iii) $∠ A B D = ∠ B A C$

Open in App

Solution

In $△ A B D$ and $△ B A C$ ,

$A D = B C$ (Given)

$∠ D A B = ∠ C B A$ (Given)

$A B = B A$ (Common)

$∴ △ A B D ≅ △ B A C$ (By SAS congruence rule)

$∴ B D = A C$ (By CPCT)

And, $∠ A B D = ∠ B A C$ (By CPCT)

Suggest Corrections

thumbs-up

8

mid-banner-image

mid-banner-image

Similar questions

A B C D

is quadrilateral in which

A D = B C

∠ D A B = ∠ C B A

. Prove that
(i)

Δ A B D = Δ B A C

B D = A C

∠ 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

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

(i) ΔABD ≅ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

$A B C D$ 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 $A D = B C$ and $∠ D A B = ∠ C B A$ . Prove that $∠ A B D = ∠ B A C$ .

View More

similar_icon

Related Videos

lock

Perpendicular Bisector

MATHEMATICS

Watch in App

Explore more

NCERT - Standard IX

Proof for Validity of Construction of a Perpendicular Bisector

Standard IX Mathematics