Question

find it and prove it is a isosceles

Answer 1

Hi friend
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Your answer
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Given that : - BD and CE are attitudes of the ∆ABC, and BD = CE.

To prove : - ∆ABC is an isosceles triangle.

Then,
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In ∆BEC and ∆BDC, we have ,
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CE = BD (Given)

BC = BC (Common)

Angle BEC = Angle BDC (90° each)

So, ∆BEC is congruent to ∆BDC .(By S.A.S. criteria)

So, Angle EBC = Angle DBC (By C.P.C.T.)

Therefore,
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In ∆ABC , Angle B = Angle C

Therefore, ∆ABC is an isosceles triangle because the base angles are equal so , AB = AC.

PROVED.

HOPE IT HELPS