Q.1. In the figure (i) and (ii), DE is parallel to BC. Find: (a) EC in figure-i (b) AD in figure –ii; Q. 2. E and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases, state whether EF is parallel to QR: (i) PE = 3.9cm, EQ = 3cm, PF = 3.6cm and FR = 2.4cm. (ii) PE = 4cm, QE = 4.5cm, PF = 8cm and RF = 9cm. (iii) PQ = 1.28cm, PR = 2.56, PE = 0.18cm and PF = 0.36cm; Q. 3. In the figure, if LM is parallel to CB and LN is parallel to CD, prove that AM/AB = AN/AD; Q. 4. In the figure, DE is parallel to AC and DF is parallel to AE. Prove that BF/FE = BE/EC; Q. 5. In the figure, DE is parallel to OQ and DF is parallel to OR. Show that EF is parallel to QR.; Q. 6. A, B and C are points on OP, OQ and OR respectively such that AB is parallel to PQ and AC is parallel to PR. Show that BC is parallel to QR.; Q. 7. Using the Thales theorem (theorem- 6.1), prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. [Recall that you have proved it in Class IX]; Q. 8. Using the converse of the Thales theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.[Recall that you have proved it in Class IX]; Q. 9. ABCD is a trapezium in which AB is parallel to DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO.; Q. 10. The diagonals of a quadrilateral ABCD intersect each other at a point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.
