Question

ABC is a triangle in which AB=AC.If the bisectors of angle B and angle C meet AC and AB in D and E respectively, prove that BD=CE​

Answer 1

Answer:

AB=AC

EC is bisector of ∠C

BD is bisector of ∠B

(i) AB=AC→∠B=∠C (isosceler triangle)

in ΔDBC and ΔECB

BC→commonside ..(1)

∠DBC=1/2∠B=1/2∠C (∵∠B=∠C)

∠ECB=1/2∠B

⇒∠DBC=∠ECB ...(2)

∠EBC=∠B=∠C=∠DBC

⇒∠EBC=∠DCB ...(3)

From (1), (2) & (3)

ΔDBC≅ΔECB

⇒BD=CE (∵ΔDBC≅ECB)

Answer 2

Answer

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