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)`

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

PQR is a triangle right angled at P and M is a point on QR such that PM bot QR . Show that PM^(2) = QM .MR.

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

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

The diagonals of a parallelogram PQRS are along the lines x+3y =4 and 6x-2y = 7, Then PQRS must be :

In triangle Delta PQR , E and F are points on the sides PQ and PR respectively. State whether EF ||QR or not? (iii) PQ = 1.28 cm PR = 2.56 cm PE = 0.18 cm and PF = 0.36 cm

Points X and Y are taken on the sides QR and RS, respectively of a parallelogram PQRS, so that QX=4XR and RY=4YS The line XY cuts the line PR at Z Find the ratio PZ: ZR

(i) Keep a glass slab on a blank paper and draw its outline PQRS as shown in the figure. (ii) Draw an inclined straight line on the side of PQ so that it intersect PQ at N. Pierce two pins vertically at two points A and B along the line. (iii) Look at the pins A and B from the opposite side of the slab and pierce pins C and D vertically so that the images of A and B are in line with C and D. (iv) Now remove the chip and the pins and draw a straight line going through points C and D so that it intersects SR at M. (v) Join points M and N. Observe the incident ray AN and emergent ray MD. Questions: (a) What is your observation about the emergent ray and incident ray ?

in the adjoining figure, Delta PQR is an equilateral triangle. Point S is on seg QR such that QS = 1/3 QR , Prove that 9 PS^(2) = 7 PQ^(2)

Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as) be distinct points on the parabola y^(2)=4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0). If st=1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is