You visited us 3 times! Enjoying our articles? Unlock Full Access!

SSS Similarity

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

Open in App

Solution

In $△ A B D, △ B A C$
$A D = B C$
$∠ D A B = ∠ C B A$
$A B = B A$
By $S . A . S$ criteria of congruency
$△ A B D ≅ △ B A C$
$⟹ B D = A C$ ...CPCT
$⟹ ∠ A B D = ∠ B A C$ ...CPCT

Suggest Corrections

Similar questions

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 B C D

A D = B C

∠ D A B = ∠ C B A

△ 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

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

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

Join BYJU'S Learning Program