Plzz Answer.

Asked by masara | 28th Dec, 2009, 02:56: PM

Expert Answer:

 

Let AD, BE and CF be the altitudes.

Then in BFC and BEC

BC is common

BFC = BEC         (Each 90o)

FC = BE (altitudes are equal)
BFC BEC                (RHS)

FBC = ECB            (By c.p.c.t)

Therefore, ABC = ACB          

i.e AB = AC        (Sides opposite to equal angles)

Similarly, ADC AFC

FAC = DCA            (By c.p.c.t)

Therefore, BAB = BCA          

i.e AB = BC      (Sides opposite to equal angles)

Hence, AB = BC = AC.

So, the triangle is an equilateral triangle.

 

 

 

Answered by  | 28th Dec, 2009, 03:30: PM

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