if a line intersects sides AB and AC of a `DeltaABC` at D and E respectively and is parallel to BC, prove that `(AD)/(AB)=(AE)/(AC)` (see Fig. 6,13).

In Fig. , sides AB and AC of DeltaABC are extended to points P and Q respectively. Also anglePBC AB .

In Fig. , sides AB and AC of DeltaABC are extended to points P and Q respectively. Also anglePBC AB .

A line parallel to BC of a triangle ABC, intersects AB and AC at D and E respectively. Prove that (AD//DB) =( AE//EC) .

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

ABCD is a trapezium with AB II DC, E and F are paints on non-parallel sides AD and BC respectively such that EF is parallel to AB Show that (AE)/(ED)=(BF)/(FC) .

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

E and F are the mid points of non-parallel sides AD and BC respectively of a trapezium prove that EF||AB.

In fig. if AC=BD, then prove that AB=CD

D and E are points on sides AB and AC respectively of a DeltaABC such that ar (DeltaBCE) = ar (DeltaBCD) . Show that DE || BC .