In fig. if PQ||BC and PR||CD prove that
`(i) (AR)/(AD)=(AQ)/(AB) (ii) (QB)/(AQ)=(DR)/(AR)`.

In figure DE|| BC and CD||EF. Prove that AD^(2)=AB xx AF .

In the figure, if BD bot AC and CE bot AB , prove that (i) Delta AEC~ Delta ADB " " (ii) (CA)/(AB)=(CE)/(DB)

In angle ACD=90^(@) and CD bot AB . Prove that (BC^(2))/(AC^(2))=(BD)/(AD)

ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB. Prove that (i) ar (ABCD) = ar(ABEF) (ii) ar (ABCD) = AB xx DG

In AD bot BC , prove that AB^(2)+CD^(2)=BD^(2)+AC^(2)

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

In the given fig. if AD bot BC Prove that AB^(2) + CD^(2) = BD^(2) + AC^(2) .

In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1. Prove that (i) 9 AQ^(2) = 9AC^(2) + 4BC^(2) (ii) 9BP^(2) = 9BC^(2) + 4AC^(2) (iii) 9 (AQ^(2) + BP^(2)) = 13 AB^(2)

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that (i) ar(PQRS) = ar(ABRS) (ii) ar(DeltaAXS) =1/2 ar(PQRS)

In the adjoining figure , seg PQ || AB. Seg PR || seg BD. Prove that QR||AD.