In Figure, `P O Q` is a line. Ray `O R` is perpendicular to lien `P QdotO S` is another ray lying between rays `O P\ a n d\ O Rdot` Prove that `/_R O S=1/2(/_Q O S-/_P O S)`

In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that /_R O S=1/2(/_Q O S-/_P O S)dot

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

A B C D is a parallelogram whose A C\ a n d\ B D intersect at Odot A line through O intersects A B\ a t\ P\ a n d\ D C\ at Qdot Prove that a r\ (\ P O A)=\ a r\ (\ Q O C)dot

In Fig. 4.90, if P S Q R , prove that P O S ~ R O Q . (FIGURE)

P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State the measure of /_P O Q

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 Figure, /_Q P R=\ /_P Q R\ a n d\ M\ a n d\ N are respectively on sides Q R\ a n d\ P R of P Q R\ such that Q M=P Ndot Prove that O P=O Q , where O is the point of intersection of P M\ a n d\ Q N

Write the equation of lines p,q,r o* s drawn in the following graph.Also find the area enclosed between them.

In Fig. 4.90, if P O S ~ R O Q , prove that P S Q R . (FIGURE)