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

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.

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 .

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 .

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 .

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) .

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 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 .

A D\ a n d\ B E are respectively altitudes of A B C such that A E=B D . Prove that A D=B E .

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles.