IUL II meet CD produced at G.] 12. Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. I know A BITO TA2010 LAB=90 14. P and Q are points on onnosite sides and

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

AB,CD are two parallel lines and a transversal l intersects AB at X and CD at Y Prove that the bisectors of the interior angles form a parallelogram,with all its angles right angles i.e.,it is a rectangle.

In parallelogram ABCD, the bisector of angle A meets DC at P and AB = 2AD. Prove that : (i) BP bisects angle B. (ii) Angle APB = 90^(@)

Crossword Puzzle Solve the given crossword and then fill up the given boxes (on the next page). Clues are given below for across as well as downward filling. Also, for across and down clues, clue number is written at the corner of the boxes. Answers of clues have to be filled up in their respective boxes. Clues Across 1. A quadrilateral with pair of parallel sides. 2. A simple closed curve made up of only line segments. 3. A quadrilateral which has exactly two distinct consecutive pairs of sides of equal length. 4. A line segment connecting two non-consecutive vertices of a polygon. 5. The diagonals of a rhombus are _________ bisectors of one another. 6. The ___________ sides of a parallelogram are of equal length. 7. The number of sides of a regular polygon whose each exterior angle has a measure of 450. 8. The sum of measure of the three angles of a _________________ is 1800. 9. A polygon which is both equiangular and equilateral is called a _________ polygon. 10. Number of sides of a nonagon. Down 11. Name of the figure 12. The ___________ angles of a parallelogram are supplementary. 13. A ______________ is a quadrilateral whose pair of opposite sides are parallel. 14. The diagonals of a rectangle are of _______________ length. 15. A five sided polygon. 16. The diagonals of a parallelogram _____________ each other. 17. A quadrilateral having all the properties of a parallelogram and also that of a kite.

In the alongside diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD. Show that: (i) anglePSB+angleSPB=90^(@) (ii) anglePBS=90^(@) (iii) angleABC=90^(@) (iv) angleADC=90^(@) (v) angleA=90^(@) (vi) ABCD is a rectangle thus, the bisectors of the angles of a parallelogram enclose a rectangle.

In a quadrilateral ABCD angle bisector of angleB and angleD are meeting at point P and Q respectively on extended sides of CD and AB. Then how angleP and angleQ, angleABC and angleaADC are related.

Through the mid point P of the side AD of a parallelogram ABCD, straight line BP is drawn cutting AC at R and CD produced at Q. Prove that bar(QR)=2bar(RB) .

P is the mid point of the side CD of a paralellogram ABCD, a line thorugh C parallelogram to PA intersects AB at Q and DA produced by A. Prove that DA=AR and CQ=QR.