Question

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Answer 1

$\textbf{\huge{ANSWER:}}$

We're Given that:

In triangle ABC,

(1) BD = CE

(2) Both BD and CE are perpendiculars on sides AC and AB, respectively.
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Answer (i) :

In triangle ABD and triangle ACE;

(i) Angle A = Angle A ( Common angle in both the triangles )

(ii) BD = CE ( We're already given with it )

(iii) Angle E = Angle D ( As BD and CE are perpendiculars and thus, they make an angle of 90° )

Therefore,

Triangle ABD is congruent to Traiangle ACE by AAS criterion of congruence.

Hence Proved!
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Answer (ii) :

As we've proved that:

Triangle ABD is congruent to Traiangle ACE by AAS criterion of congruence, then:

AB = AC ( Congruent Parts of Congruent Triangles {C.P.C.T.} )

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Answer 2

so we can prove very easily that ∆ABC is isosceles triangle