Question

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Answer 1

Answer:

option a is write answer

Answer 2

Answer:

(4) option is correct

Step-by-step explanation:

Given that,

$\rm\longrightarrow\: \angle\: BAD\: =\: \angle \:EAC$

add ∠ DAC both sides

$\rm\longrightarrow\: \angle\: BAD\: +\:\angle \:DAC\:=\: \angle \:EAC+\angle\;DAC$

$\rm\longrightarrow\: \angle\: BAC\: =\: \angle \:DAE$

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Now consider ∆ ABC and ∆ ADE

$\rm\bullet\quad AB\: =\:AD\qquad[\:Given\:]$

$\rm\bullet\quad \angle\: BAC\: =\: \angle \:DAE\qquad[\: Proved\: Above\:]$

$\rm\bullet\quad AC\: =\:AE\qquad[\:Given\:]$

Hence by the congruency criteria of SAS ( Side Angle Side ) we can conclude that ∆ABC is congruent to ∆ADE.

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Now by the rule of CPCT ( corresponding part of congruent triangle ), we can conclude that,

$\rm\bullet\quad\angle \:ADE\:=\:\angle\:ABD$

$\rm\bullet\quad BC\:=\:DE$

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Hence both option (1.) and (2.) are correct.