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

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

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

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In Figure, P Q R S is a quadrilateral. P Q is its longest side and R S is its shortest side. Prove that /_R > /_P a n d /_S > /_Q Given : P Q R S is a quadrilateral. P Q is its longest side and R S is its shortest side. To Prove : (i) /_R > /_P (ii) /_S > /_Q Construction : Joint P R a n d Q S

In Fig. 4.238, S and T are points on the sides P Q and P R respectively of P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of P S T and P Q R . (FIGURE)

In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of /_P Q R and /_P R S meet at point T, then prove that /_Q T R=1/2/_Q P R .

In figure PS is the bisector of /_Q P R of DeltaP Q R . Prove that (Q S)/(S R)=(P Q)/(P R) .

In Figure, P Q R S is a parallelogram, P O\ a n d\ Q O are, respectively, the angle bisectors of /_P\ a n d\ /_Q . Line L O M is drawn parallel to P Q . Prove that: P L=Q M (ii) L O=O M

In Figure, P Q R S is a square and T\ a n d\ U are, respectively, the mid-points of P S\ a n d\ Q R . Find the area of O T S\ if P Q=8\ c mdot

In Fig. 6.39, sides QP and RQ of DeltaP Q R are produced to point S and T respectively. If /_S P R=135^@ and /_P Q T=110^@ , find /_P R Q.