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

Opposite Sides of a Parallelogram Are Equal

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 $B D = A C .$

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 side ]

So, by the Side-Angle-Side criterion of congruence,
$△ A B D ≅ △ B A C$

$∴$ $B D = A C$ [CPCT]

Suggest Corrections

Similar questions

A D = B C

∠ D A B = ∠ C B A

△ A B D ≅ △ B A C

B D = A C

∠ A B D = ∠ B A C

A B C D

A D = B C

∠ D A B = ∠ C B A

△ A B D ≅ △ B A C

A B C D

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

A D = B C a n d ∠ D A B = ∠ C B A

A D = B C a n d ∠ D A B = ∠ C B A

Join BYJU'S Learning Program