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

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 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, 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 Q R S is a parallelogram. If X\ a n d\ Y are mid-points of P Q\ a n d\ S R respectively and diagonal S Q is jointed. The ratio a r\ (^(gm)\ X Q R Y):\ a r\ ( Q S R)= 1:4 (b) 2:1 (c) 1:2 (c) 1:2 (d) 1:1

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)

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 the figure ABCD iś a parallelogram. dotP, Q, R and S are the midpoint of the sides of the parallelogram. Prove that P Q=R S and Q R=P S .