In the quadrilateral ACBD, AB is a diagonal. If AC = AD and AB bisects $∠ A$ , by which congruence property is $Δ A C B ≅ Δ A D B$ ?

S.A.S.

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A.S.A.

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S.S.S.

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R.H.S.

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Solution

The correct option is A S.A.S.
In $Δ A C B$ and $Δ A D B$ ,

AC = AD (Given)
$∠ C A B = ∠ D A B (A B b i s e c t s ∠ A)$
and AB = AB (Common side)
$∴ Δ A C B ≅ Δ A D B$ (S.A.S rule)

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Similar questions

∠ A

Δ A C B ≅ Δ A D B

A C B D, A C = A D

A B

∠ A

In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

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

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