In the given figure- if - BAD - CAD - - ABD - ACD- then which of the following is true -A- ABD - ACD by SAA postulateB- ABD - ACD by AAS postulateC- AB - ACD- B D-C D

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AAS Criteria for Congruency

In the given ...

Question

In the given figure, if $∠ B A D = ∠ C A D, ∠ A B D = ∠ A C D,$ then which of the following is true ?

$△ A B D ≅ △ A C D$ by SAA postulate

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$△ A B D ≅ △ A C D$ by AAS postulate

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AB = AC

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BD = CD

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Solution

The correct options are
B
$△ A B D ≅ △ A C D$ by AAS postulate

C
AB = AC

D
BD = CD

In $△ A B D$ and $△ A C D$

(i) $∠ A B D = ∠ A C D$ ........(given)

(ii) $∠ B A D = ∠ C A D$ .....(given)

(iii) AD = AD ............(common)

(iv) $△ A B D ≅ △ A D C$ ........(AAS Postulate)

(v) AB = AC ......(cpct)

(vi) BD = CD .......(cpct)

Hence (B), (C) and (D)

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Similar questions

In the given figure, if $∠ B A D = ∠ C A D, ∠ A B D = ∠ A C D,$ then which of the following is false?

In the given figure, if $∠ B A D = ∠ C A D, ∠ A B D = ∠ A C D,$ then which of the following is false?
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