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

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that: C Q=1/3B Cdot Prove that A Q C P is a parallelogram.

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

A B C D is a parallelogram. P is the mid-point of A BdotB D\ a n d\ C P intersect at Q such that C Q : Q P=3: 1. If a r\ ( P B Q)=10\ c m^2, find the area of parallelogram A B C D

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, P S D A is a parallelogram in which P Q=Q R=R S\ a n d\ A P B Q C Rdot Prove that a r\ (\ P Q E)=\ a r\ (\ C F D)dot

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

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d\ A B when produced meet at Fdot Then A F= 3/2A B (b) 2\ A B (c) 3\ A B (c) 5/4\ A B

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C