Question

BD and CE are bisectors of angle B and angle C of an isosceles ∆ABC with AB =AC. Prove that BD =CE ​

Answer 1

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Answer 2

Answer:according to isosceles traingle property equal sides have equal opposite angles

therefore, ∠ABC = ∠ACB                         (1)

dividing both angles by 2  .....∠ABC /2= ∠ACB/2

then, ∠DBC = ∠ECB       (since BD and CE are angle bisectors which means it divides the triangle into two equal halves)      (2)

given, AB = AC                                             (3)

now in triangle EBC and DCB

BC = BC           (common base)

∠EBC = ∠DCB        ( by 1)

∠BCE = ∠DBC        ( by 2 )

then by ASA congruence criterion, we have ΔEBC ≅ ΔDCB

CE = BD   [∵ Corresponding parts of congruent triangles are equal] or, BD = CE ∴

Step-by-step explanation: