ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that
(i) `DeltaAPB ~= DeltaCQD`
(ii) `AP = CQ`

ABCD is a parallelogram and AP and CQ are perpendiculars from vertex A and C on diagonal BD. Show that (i) DeltaAPB~=DeltaCQD (ii) AP=CQ .

Diagonal AC of a parallelogram ABCD bisects angleA . Show that (i) it bisects angleC alo (ii) ABCD is a rhombus.

Let ABCD be a parallelogram the equation of whose diagonals are AC : x+2y =3 ; BD: 2x + y = 3. If length of diagonal AC =4 units and area of ABCD = 8 sq. units. (i) The length of the other diagonal is (ii) the length of side AB is equal to

Let ABCD be parallelogram whose equations for the diagonals AC and BD are x+2y=3 and 2x+y=3, respectively. If length of diagonal AC=4 units and area of parallologram ABCD=8 sq. units then (i)the length of other diagonal BD is (a) 10/3 (b) 20/3 (c) 2 (d) 5 (ii) length of side AB equals to (a) (2sqrt(58))/3 (b) (2sqrt(58))/9 (c) (3sqrt(58))/9 (d) (4sqrt(58))/9

(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, seg AB is a diameter of a circle with centre C . Line PQ is a tangent, it touhces the circle at T. segs AP and BQ are perpendiculars to line PQ. Prove seg CP ~= seg CQ .

Figure shows a square loop of edge a made of a uniform wire. A current i enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it.

Tangents are drawn from the point (17, 7) to the circle x^2+y^2=169 , Statement I The tangents are mutually perpendicular Statement, lls The locus of the points frorn which mutually perpendicular tangents can be drawn to the given circle is x^2 +y^2=338 (a) Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statementl (b)Statement I is correct, Statement I| is correct Statement II is not a correct explanation for Statementl (c)Statement I is correct, Statement II is incorrect (d) Statement I is incorrect, Statement II is correct

The figure showing nephridial system of earthworm is given here. Identify the types of nephridia labelled as A, B and C from the list (i) to (iii) given below and select the correct option (i) Septal nephridia (ii) Integumentary nephridia (iii) Tufts of pharyngeal nephridia