In ` A B C ,D` is the mid-point of `A B ,P` is any point of `B C, C Q || P D` meets `A B` in `Q` . Show that `a r( B P Q)=1/2a r( A B C)dot` TO PROVE : `a r( B P Q)=1/2a r( A B C)` CONSTRUCTION : Join CD.

In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D meets A B in Q . Show that a r( B P Q)=1/2a r( A B C)dot

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 is the mid-point of B C , ,Q is the mid-point of A P , such that B Q produced meets A C at Rdot Prove that 3RA= CA

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ (triangle \ P R Q)=1/2a r\ (triangle \ A R C) .

If Delta A B C ~ Delta P Q R such that a r( A B C)=4a r( P Q R)dot If B C=12 c m , then Q R=

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A parallel to C P meets C B produced in Q and the parallelogram P B Q R completed. Show that a r(llgm A B C D)=a r(llgm B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(llgm A B C D)=a r(llgm B P R Q)

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A parallel to C P meets C B produced in Q and the parallelogram P B Q R completed. Show that a r(^(gm)A B C D)=a r(^(gm)B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(^(gm)A B C D)=a r(^(gm)B P R Q)

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ ( triangle R Q C)=3/8\ a r\ (triangle \ A B C) .

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)