Question

in the given figure, e is any mid point on median ad of a triangle ABC. show that ar(Abe) = ar(ace)

Answer 1

in triangle ABC,
AD is the median of triangle ABC.
so, ar(abd)=ar(acd)
now e is the mid point
ae =ed
so ed is also a median of triangle BEC.
so, ar(bed)=ar(ced)
now, ar(abd) =ar (acd)
ar(abd) -ar(bed)=ar(acd)-ar(bed). (subst ar(bed) both sides.because
ar( bed)=ar(ced). )
after subtraction,
ar(Abe)=ar( ace)
hence, proved.

thanks for question.