In Figure, `A B C D` is a parallelogram and `/_D A B=60^0dot` If the bisectors `A P` and `B P` of angles `A` and `B` respectively, meet at `P` on `C D ,` prove that `P` is the mid-point of `C Ddot`

In Figure, A B C D is a parallelogram and /_D A B=60^0dot If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D

In Figure, A B C D is a parallelogram and X ,Y are the mid=points of sides A B and D C respectively. Show that A X C Y is a parallelogram. Figure

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D P Q) CONSTRUCTION : Join A Cdot

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

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.

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D) GIVEN : A parallelogram A B C D in which X and Y are the mid-points of B C and C D respectively. TO PROVE : a r( A X Y)=3/8a r(^(gm)a b c d) CONSTRUCTION : Join B Ddot

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot