In figure,
$B D$ is a bisector of $∠ B, C D = D A$
In order to show the $△ B D A$ and $△ B D C$ are congruent, which property of triangle applies here?

S A S

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S S S

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A A S

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None

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Solution

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

$B D$ is a bisector of $∠ B$
$B D$ is common side.
$∠ A B D = ∠ C B D$
$C D = D A$

Two triangles are congruent from $S A S$ postulate

Hence option A is correct.

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Similar questions

In $Δ$ ABD, AB=AD and AC is perpendicular to BD. State the property by which $Δ$ ACB $≅$ $Δ$ ACD.

(a) DA bisects $∠ B A C$ and $∠ B = ∠ C$ . Prove that $Δ B D A ≅ Δ C D A$ .

(b) If these triangles are congruent, choose the property by which they are congruent.

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In the given figure it is given that AB = CF, EF = BD and $∠$ AFE = $∠$ DBC. Then $△$ AFE is congruent to $△$ CBD by which criterion?

Q. In the given figure AE is bisector of

∠ B A C

and of

∠ B D C

. show that

Δ A B D ≅

ACD and hence BD = CD

In the given figure, if $∠ B A D = ∠ C A D, ∠ A B D = ∠ A C D,$ then which of the following is false?
a) $△ A B D ≅ △ A C D$ by SAS postulate
b) $△ A B D ≅ △ A C D$ by AAS postulate
c)AB = AC
d)BD = CD

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In figure,BD is a bisector of ∠B,CD=DAIn order to show the △BDA and △BDC are congruent, which property of triangle applies here?

The correct option is A SASIn △ABD and △CBDBD is a bisector of ∠BBD is common side.∠ABD=∠CBDCD=DATwo triangles are congruent from SAS postulateHence option A is correct.

In figure,
$B D$ is a bisector of $∠ B, C D = D A$
In order to show the $△ B D A$ and $△ B D C$ are congruent, which property of triangle applies here?

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

$B D$ is a bisector of $∠ B$
$B D$ is common side.
$∠ A B D = ∠ C B D$
$C D = D A$

Two triangles are congruent from $S A S$ postulate

Hence option A is correct.