Let $A B C D$ be a quadrilateral in which $△ A B D ≅ △ B A C$ . Prove that $A B C D$ is a parallelogram.

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Solution

Given: $A B C D$ is a Quadrilateral

$Δ A B D ≅ Δ B A C$

To prove: $A B C D$ is a parallelogram

$B D = A C$ (CPCT)

Therefore, Area of $Δ A B D =$ Area of $Δ B A C$

And both the triangles stand on same base $A B$ .

$⸫ D C | | A B$

But $A D | | B C$

$⸫ A D | | B C$

Therefore, opposite sides are parallel

Hence, $A B C D$ is a parallelogram

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Let ABCD be a quadrilateral in which ∠A = ∠C, and ∠B = ∠D. Prove that ABCD is a parallelogram.

$A B C D$ 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 $∠ A B D = ∠ B A C$ .

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

∠ D A B = ∠ C B A

∠ A B D = ∠ B A C .

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