Question

plz answer my question

Answer 1

aloha!

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here is the answer:

given: BE = CF = AD
to prove: ∆ABC is equilateral
proof: ar∆ ABC = 1/2 × BC × AD-------(1)
ar∆ ABC = 1/2 × AC × EB---------(2)
ar∆ ABC = 1/2 × AB × CF---------(3)

since, 1,2 and 3 are same we can write

BC × AD = AC × EB = AB × CF
BC × AD = AC × AD = AB × AD ( altitudes are given to be equal )
so,
we can say

BC = AC = AB

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hope it helps :^)

Answer 2

Answer:

given =AD = BE = CF

which means ares is dependent on only 2 factors base and altitude..

since area of a triangle will always be equal irrespective of which side u take as base..

let base1 has altitude1 as perpendicular and same for rest all..

i can say base1*altitude1 = base2*altitude2 = base3*altitude3 since half is a constant i ignored it

since altitudes are all equal .. bases are bound to be equal if we say area is equal.

hence all sides will be equal making triangle an equilateral triangle..