In Figure, `P Q R S` and `A B R S` are parallelograms and `X` is any point on side `B R`. Show that : `a r(||^(gm)P Q R S)=a r(||^(gm)A B R S)`, `a r(triangle A X S)=1/2a r(||^(gm) P Q R S)`

In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) a r(P Q R S) = a r(A B R S) (ii) a r(A XS)\ =1/2 ar(P Q R S)

In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >2P S

In figure, P Q=P R . Show that P S > P Q .

In Figure, P Q R S is a square. Determine /_S R Pdot

In Figure, P is a point in the interior of a parallelogram A B C Ddot 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)

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 Figure, O P||R S . Determine /_P Q R

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 Figure , find out /_P X R , if P Q || R S .

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .