If a line intersects sides AB and AC of a `DeltaA B C`at D and E respectively and is parallel to BC, prove that `(A D)/(A B)=(A E)/(A C)`

If a line intersects sides AB and AC of a Delta ABC at D and E respectively and is parallel to BC, prove that (AD)/(AB)=(AE)/(AC)

The vertices of A B C are A(4,\ 6),\ \ B(1,\ 5) and C(7,\ 2) . A line is drawn to intersect sides A B and A C at D and E respectively such that (A D)/(A B)=(A E)/(A C)=1/4 . Calculate the area of A D E and compare it with the area of A B C .

The vertices of a DeltaABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively, such that (AD)/(AB)=(AE)/(AC)=1/4 Calculate the area of the DeltaA DE and compare it with the area of DeltaABC

In Fig. 7.48, sides AB and AC of DeltaA B C are extended to points P and Q respectively. Also, /_P B C\ \ A B .

A triangle ABC (with usual notations) is a right angled isosceles triangle right angled at B. Let a line isdrawn passing through the centroid 'G' of the triangle and parallel to BC intersecting sides AB and AC at D and E respectively, if length of BC = 9, then the area of quadrilateral ADGF (where F is the midpoint of AC) is

A straight line parallel to the base BC of the triangle ABC intersects AB and AC at the points D and E respectively. If the area of the Delta ABE be 36 sq. cm, then the area of the Delta ACD is

In the adjoning figure, D and E are the points on the sides AB and AC respectively of Delta ABC and area of Delta BCE = " area of " Delta BCD . Prove that DE ||BC

D and E are points on sides AB and AC respectively of Delta ABC such that ar( Delta DBC) = ar( Delta EBC). Prove that DE I I BC.

In triangle ABC , sides AB and AC are extended to D and E, respectively, such that AB=BD and AC =CE , Find DE, if BC=6 cm .