In the given $A D = B E$ and $∠ D A B = ∠ E B A$ . Which of the following statements are true?

$Δ D A B ≅ Δ E B A$ by SAS postulate

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$Δ D A B ≅ Δ E B A$ by ASA postulate

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$Δ D A B ≅ Δ E B A$ by AAS postulate

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$B D = A E$

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Solution

The correct options are
A
$Δ D A B ≅ Δ E B A$ by SAS postulate

D
$B D = A E$

In $Δ D A B$ and $Δ E B A$

(i) $A D = B E$ ………(given)

(ii) $∠ D A B = ∠ E B A$ ……….(given)

(iii) $A B = A B$ ………(common)

$∴ Δ D A B ≅ Δ E B A$ … (SAS postulate)

$\Rightarrow B D = A E$ (CPCT)

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