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Nikhitabisht
@Nikhitabisht
June 2022
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9. D and E are points on sides AB and AC respectively of triangle ABC such that ar (ABC) = ar (EBC). Prove that DE is parallel to BC.
Answers & Comments
amisha1506
I think u mean to say a(DBC)=a(EBC)
SO,
A(DBC)= 1/2*BC*H1
A(EBC)= 1/2*BC*H2
A(DBC)= A(EBC)
1/2*BC*H1= 1/2*BC*H2
H1=H2
As both d vertices are at equal distance from the base, therefore both the points r equidistant from d base and hence BC//DE
5 votes
Thanks 6
Nikhitabisht
thanx
amisha1506
my pleasure!!
Nikhitabisht
: )
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Answers & Comments
SO,
A(DBC)= 1/2*BC*H1
A(EBC)= 1/2*BC*H2
A(DBC)= A(EBC)
1/2*BC*H1= 1/2*BC*H2
H1=H2
As both d vertices are at equal distance from the base, therefore both the points r equidistant from d base and hence BC//DE