POTENTIAL ANALYSIS

POTENTIAL ANALYSIS

QUADRILATERALS TOTAL MARKS: 50 TIME: 90 MIN SACTION A MARKS 1 (13 x 1=13)1. Can all angles of a quadrilateral be right angles? Give reason for your answer.2. Can the angle of a quadrilateral be 115o, 85o , 75 o,80o?3. The diagonals of a quadrilateral ABCD are equal. It is necessarily a parallelogram.4. In fig. ABCD and AEFG are two parallelograms. If angle C is 50o, Determine angle F.

5. In fig. BDEF and FDCE are parallelograms. Can you say that BD=CD?

6. In the given figure 2.3 ABCD is a IIgm . find x and y

7. ABCD is a IIgm In which angle ADC is 75oand side AB is produced to E as shown in figure ,find (x + y)

8. In figure, PQRS is a IIgm in which angle 130o. Find angle RQT

9. In fig 2.10, ABCD is a rhombus. If angle ABD is 40o.Find the value of y.

10. Two opposite angle of IIgm are (60-x) and (3x-4).Find the measure of each angle of IIgm.11. ABCD is IIgm. If its diagonal are equal, then find the value of angle ABC.12. In a IIgm ABCD, if angle A is 75o, Find angle C.13. PQRS is a square. PR and SR intersect at O. State the measure of angle POQ.

SECTION B 2 MARKS (7x2=14)

14. In Triangle ABC, median AM is produced to D such that AM=MD fig 2.15. Prove that ABCD is IIgm.

15. Bisector of two adjacent angle A and B of quad. ABCD intersect at a point O. Prove that 2 AOB= C + D16. In a IIgm show that the angle bisector of two adjacent angles intersect at right angle.17. ABCD is IIgm and line segment AX, CX bisect angle A and C respectively. Show that AX II CY (fig 2.23)

18. In fig D, E and F are the mid points of the sides BC, CA and AB respectively of Triangle ABC. If AB=6.2 cm, BC=5.6 Cm and CA=4.6cm. Find the parameter of(I) trapezium FBCE (II) (ii) triangle DEF.

19. In fig 2.27, D is the midpoint of AB and PC=, AP= 3cm.If AD=BD=4 cm and DE II BP. Find AE.

20. In fig side AC of triangle ABC produced to E so that CE=AC.D is the midpoint of BC and ED produced meets AB at F. RC,DP is drawn parallel to BA. Prove that FD=FE.

SECTION C 3 MARKS (3 x 5= 15)

21. In fig, P is the midpoint of the sides BC of IIgm ABCD, such that angle 1= angle 2. Prove that AD= 2 CD

22. In fig , ABCD is IIgm and P and Q are the points on the diagonal BD such that BQ = DP. Show that APCQ is a IIgm.

23. In fig , AM and CN are perpendiculars to the diagonal BD of a IIgm ABCD. Prove that AM=CN.

24. Prove that, the bisector of any two consecutive angles of parallelogram intersect at right angle.25. D, E and F are the midpoint of sides BC, CA and AB, respectively of an equilateral triangle ABC. Show that triangle DEF is also equilateral triangle.

SECTION C 3 MARKS (2 x 4= 8)26. Prove that the bisector of the angle of parallelogram enclosed a rectangle.27. ABCD is a IIgm in which P and Q are the midpoints of the opposite sides AB and CD. If AQ intersects DP at S and BQ intersect CP at R, show that (i)APCQ is IIgm.(ii)DPBQ is IIgm.(iii)PSQR is IIgm. A.M.I. COACHING CENTREPage 2