D and E are points on sides AB and AC respectively of `DeltaA B C` such that`a r"\ "(D B C)"\ "="\ "a r"\ "(E B C)` . Prove that `D E"\ "||"\ "B C` .

D and E are points on sides AB and AC respectively of DeltaA B C such thata r" "(D B C)" "=" "a r" "(E B C) . Prove that D E" "||" "B C .

D and E are points on sides AB and AC respectively of Delta A B C such that a r\ (D B C)\ =\ a r\ (E B C) . Prove that D E||B C .

In Figure, D , E are points on sides A B and A C respectively of /_\A B C , such that a r( B C E)=a r( B C D) . Show that DE||BC .

If D and E are points on sides A B and A C respectively of a triangle A B C such that D E || B C and B D=C E . Prove that A B C is isosceles.

In Figure, D , E are points on sides A B and A C respectively of A B C , such that a r( B C E)=a r( B C D)dot Show that DE ll BC .

D and E are the points on the sides A B and A C respectively of a triangle A B C such that: A D=8c m ,\ \ D B=12 c m ,\ \ A E=6c m and C E=9c m . Prove that B C=5//2\ D E .

In A B C ,\ D and E are points on sides A B and A C respectively such that A DxxE C=A ExxD B . Prove that D E B C .

In a A B C ,D and E are points on sides A B a n d A C respectively such that B D=C E . If /_B=/_C , show that DE || BC .

D and E are points on the sides A B and A C respectively of a A B C such that D E B C and divides A B C into two parts, equal in area, find (B D)/(A B) .

D and E are points on equal sides A B and A C of an isosceles triangle A B C such that A D=A E . Prove that B ,C ,D ,E are concylic.