Two triangles ABC and DBC are in the same side of the common base BC. Lines drawn parallel to BA and BD from any point E on BC intersect AC and DC at the points P and Q respectively. Show that PQ is parallel to AD.

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 12 , AP = 4 , QC = 5 then determine AQ.

A line PQ drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. AP = 1/3 PB then determine (area of ABC)/(area of APQ)

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 20 , AC = 15 and AQ = 9 then determine BP.

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AQ : QC = 7: 4 and AB = 8.8 then determine AP and PB.

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If AB = 7.2 , AC = 4.8 and AX = 4.2 then show that AY = 2.8 .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If AB = 4 , AC = 3 and AY = 1.8 then prove that BX= 1.6 .

triangleBAC and triangleBDC are two right-triangle on the same side of the base BC.If AC ans DB intersect each other at a point P,show that APxxPC=DPxxPB .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If X divides AB in 8:3 and AC = 8.8 then prove that AY = 6.4 and YC = 2.4 .

/_\PBC and /_\ QBC are two isosceles triangles on the same side of the some base. Show that the PQ is the right bisector of BC.

Of the trapezium ABCD, AB||DC and DC = 2AB. If the line segment EF drawn parallel to AB meets AD and BC at the points Fand E respectively so that (BE)/(EC)=3/4 and the diagonal DB meets EF at the points G, prove that 7FE=11AB