TESTQuadrilaterals

Max. Marks = 50Min. Time = 2 hrs

1. In a quadrilateral ABCD, CO and DO are the bisectors of / C and / D, respectively. Prove that / COD = ½ (/ A + / B ). 2 marks

2. Mark the following as True(T) or False(F)-a. In a parallelogram, the diagonals are equal.b. In a parallelogram, the diagonals intersect at 90˚.c. If 3 sides of a quadrilateral are equal, it is a parallelogram.d. If 3 angles of a quadrilateral are equal, it is a parallelogram. 2 marks

3. Write 4 conditions sufficient for a quadrilateral to be a parallelogram. 2 marks

4. In a parallelogram ABCD, the bisectors of / A also bisects BC. Prove that AD = 2AB. 2 marks

5. In parallelogram ABCD, / A= 60˚. If the bisectors of / A and / B meetat point P which lies on DC. Prove that-

a. AD = DPb. PC = BCc. DC = 2AD 3 marks

6. Give the fundamental definitions of the following quadrilaterals-a. Parallelogramb. Rhombusc. Rectangled. Squaree. Kitef. Isosceles trapezium 3 marks

7. X and Y are the mid-points of opposite sides AB & CD of a parellelogram ABCD. AY & DX intersect at P. CX & BY intersect at Q. Prove that quad. PXQY is a parallelogram. 4 marks

8. If ΔABC & ΔDEF are such that AB, BC are respectively equal and parallel toDE, EF, prove that-

a. AC = DFb. ΔABC ≡ ΔDEF 4 marks

9. P & Q are the points of trisection of diagonal BD of parallelogram ABCD. Prove that CQ is parallel to AP. Also prove that AC bisects PQ. 4 marks

10. ABCD is a rhombus. EABF is a straight line such that EA = AB = BF. Prove that ED & FC when produced meet at right angles. 4 marks

11. ΔABC is right angled at B. P is the mid-point of AC. Prove that PA = PB = PC. 4 marks

12. In ΔABC, P,Q & R are the mid-points of BC,CA & AB respectively. PR and BQ meet at X. CR and PQ meet at Y. Prove that XY=1/4 BC. 4 marks

13. In ΔABC, BE is perpendicular to AC. AD is any line from A to BC intersecting BE in H. P,Q & R are respectively the mid-points of AH, AB & BC. Prove that / PQR = 90˚. 4 marks

14. State and prove the mid-point theorem. 4 marks

15. ABCD is a trapezium in which AB|| CD & AD = BC. Prove that-a. / A = / Bb. / C = / Dc. ΔABC ≡ ΔBADd. AC = BD 4 marks

BQ. In the adjoining figure AD and BE are perpendicular to line l. If C is the mid-point . of AB, prove that CD = CE. 5 marks