Question

If two altitudes of a triangle are equal, prove that it is an
isosceles triangle.
Hint. AABD = AACE]​

Answer 1

Answer:

In a triangle ABC

ar(ABC) = 1/2. ( base × height)

= 1/2. AC × BE. -----------------(1)

similarly ,

ar(ABC) =. 1/2. ( base × height )

=. 1/2. BC × AD. -----------------(2)

From equation (1) & (2).

1/2. AC × BE. =. 1/2. BC × AD

AD. =. BE. ( Given )

AC. =. BC

Hence ,

Triangle ABC is a isosceles triangle.