Question

if the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles

Answer 1

hay!!

Dear friend -

if the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles

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Here is ur answer



Given-AΔABC in which AD is the bisector of
ㄥA which meets BC in D such that BD=DC


construction Produce AD to E such that AD= DE join EC


proof -


In ΔABD and EDC, we have :


BD=DC (given), AD=DE(by const.)


ㄥADB = ㄥEDC ( vert. opp)


ΔABD ~ ΔECD


AB= EC and ㄥ1=ㄥ3. (c.p.c.t)


Also, ㄥ1=ㄥ2. [AD= bisects ㄥA]


ㄥ2 = ㄥ3


consequently, EC = AC ( side opp.to equal)


AB = AC. [EC = AB]


Hence Δ ABC is isosceles.



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