In a quadrilateral $A C B D, A C = A D$ and $A B$ bisect $∠ A$ , then:

B C ≅ A D

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B D ≅ A C

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B C ≅ B D

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A B ≅ A C

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Solution

The correct option is C $B C ≅ B D$
In $△ A B C$ and $△ A B D$ ,

$A B = A B$ (Common)
$∠ C A B = ∠ D A B$ ( $A B$ bisect $∠ A$ )
$A C = A D$ (Given)

By using $S A S$ rule of congruence,
$△ A B C ≅ △ A B D$
$\Rightarrow B C ≅ B D$ [by $C P C T$ ]

Therefore, option $C$ is correct.

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Similar questions

A C B D, A C = A D

A B

∠ C A D .

△ A B C ≅ △ A B D

B C

B D

In quadrilateral $A C B D, A C = A D$ and $A B$ bisects $∠ A$ . Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

∠ A

△ A B C ≅ △ A B D

Δ A B C

≅

Δ A B D .

In quadrilateral $A C B D$ , $A C = A D$ and $A B$ bisects $∠ A$ (see Fig). Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

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